Project Euler with Emacs Lisp

Project Euler using Emacs Lisp

Projec Euler is a set of recreational mathematical puzzles.

These are my personal notes about using Emacs Lisp to solve Project Euler problems.

The questions are all copyright Project Euler.

The answers document my solutions using Emacs Lisp.

Elisp is so far fairly good at this, because Elisp is expressive enough for the algorithms to be pretty concise. Elisp is slow enough to make it obvious if an algorithm wasnt very clever. Since emacs-calc has bignum support I suspect that some of the solutions are a bit too easy, OTOH theres a lot of problems so I dont worry about that.

Emacs Org-mode makes it easy to keep notes and code mixed. Emacs and Lisp in general makes it faster to get to the actual problem solving rather than messing about with preparations. Often I just convert the PE input data to Lisp structures with Emacs, and keep them in the org file, rather than wasting time writing I/O code.

Overall, Emacs is a pretty efficient PE solving plattform so far.

PE notes

You can register here: http://projecteuler.net/register

A link to an individual problem looks like: http://projecteuler.net/problem=26

Progress: http://projecteuler.net/progress

To select an "easy" problem, use http://projecteuler.net/problems, and sort by "solved by". This is good for morale!

Solving problems in order to receive awards is also good for morale, so my list of problems is tagged with awards as well.

Awards

Fibonacci Fever: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 FF

Trinary Triumph: 1, 3, 9, 27, 81, 243 TT

Unlucky Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 US

Daring Dozen: 12 3-digit problems DD

easy as pi: 3, 14, 15, 92, 65, 35, 89, 79, 32, 38, 46 PI

triangle trophy: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325 TR

DONE 1: Multiples of 3 and 5 FFTTUS

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

A:

brute force: check all natural numbers between 1 ... 1000. if divisable by 3 or 5, add to sum. better: 2 loops, one step 3 one step 5. dont add 3s that are also divisable by 5, and vice versa.

1(let ((sum 0)) (cl-loop for x from 1 to 999 do (if (or (= 0(mod x 5 )) (= 0(mod x 3 ))) (setq sum (+ x sum)))) sum)

233168

DONE 2: Even Fibonacci numbers FF

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

A:

last 2 fibbonacci of the 7 first:

 1    ;;fibonaccio
 2
 3    (let ((a 1)(b 2) (c 0)) (cl-loop for x from 1 to 7 do  (setq c (+ a b) a b b c)   ) (list a b c))
 4
 5    (let ((a 1)
 6	  (b 2)
 7	  (c 0)
 8	  (sum 0))
 9      (cl-loop for x from 1 to 100000 until (< 4000000 b) do
10	       (setq c (+ a b) a b b c)
11	       (if (= 0 (mod a 2)) (setq sum (+ sum a)) ))
12      (list a b c sum))
13(3524578 5702887 5702887 4613732)

DONE 3: Largest prime factor PIFFTT

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number A= 600851475143 ?

A:

http://en.wikipedia.org/wiki/Prime_factor brute: search backwards from sqrt(A)(?), until prime. check if prime is factor of A. done, else continue search. this will be O(n2), therefore slow.

https://en.wikipedia.org/wiki/Trial_division describes some optimizations

 1    ;;this naive implementation is much faster that i thought it'd be
 2    (defun primep (p)
 3      ;;1 is not a prime, so thats not handled atm
 4      ;;(primep 1)
 5      ;;(primep -2)
 6      ;; (primep 2)
 7      ;; (primep 3)
 8      ;;(primep 4)
 9      ;; (primep 5)
10      ;;(primep 6)
11      ;; (primep 7) 11 13 17
12      (cond
13       ((<  p 2) nil)
14       (t
15	(cl-loop for x from 2 to (sqrt p)
16		 for no-remainder = (= 0 (% p x ))
17		 until no-remainder
18		 finally return (if (= 1 p) nil  (not no-remainder))))))
19
20  ;; this seems to be correct for 13195, but is too slow
21  (let ((A 600851475143 ))
22    (cl-loop for x from
23	     ;;(1-  A)
24	     ;;(truncate (1+ (sqrt A)))
25	     (truncate (/ A 2))
26	     downto 1
27	     until (and  (= 0 (% A x)) (primep x))
28	     finally return x
29
30	     ))
31
32;;lets not try every integer, instead try A/2, A/3 etc
33;; this is faster, but still a bit slow
34  (let ((A 600851475143
35
36	   ))
37    (cl-loop for x from
38	     2 to
39	     (truncate (/ A 2))
40	     until (and  (= 0 (% A x)) (primep (/ A  x)))
41	     finally return (/ A  x)
42
43	     ))
446857

DONE 4: Largest palindrome product US

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

A:

999 x 999 = 998001 100 x 100 = 10000 999 x 100 = 99900

but how do i know its palindromic efficiently? http://en.wikipedia.org/wiki/Palindromic_number

 1  (apply (lambda (x pos)(/ (% x (expt 10 pos)) (expt 10 (1- pos)))) '(12345 5))
 2  1
 3
 4(defun digit  (x pos)
 5  (/
 6   (% x
 7      (expt 10 pos))
 8   (expt 10
 9	 (1- pos))))
10
11(defun palindrom-numberp  (x)
12  (if (> x 99999)
13      (and
14       (=
15	(digit x 1)
16	(digit x 6))
17       (=
18	(digit x 2)
19	(digit x 5))
20       (=
21	(digit x 3)
22	(digit x 4)))
23    (and
24       (=
25	(digit x 1)
26	(digit x 5))
27       (=
28	(digit x 2)
29	(digit x 3)))))
30
31
32;;returns a palindrome, but the factorization isnt known. rats.
33(cl-loop for x from 99801 downto 10000
34	 until (palindrom-numberp x)
35	 finally return x)
3699799
37
38;;naive try
39(defun palindrome-find ()
40  (let ((p))
41    (cl-loop for x from 999 downto 100
42	     until (setq p (cl-loop
43			    for y from x downto 100
44			    for z = (palindrom-numberp (* x y) )
45			    until z
46			    finally return
47			    (if z
48				(list (* x y) x y))))
49	     finally return p)))
50(palindrome-find)
51(888888 924 962)
52(580085 995 583)
53(698896 836 836)
54
55its supposed to be
56(906609 913 993)
57
58(defun palindrome-find ()
59  (let ((p))
60    (cl-loop for x from 999 downto 100 do
61	     (cl-loop
62	      for y from x downto 100
63	      for z = (palindrom-numberp (* x y) ) do
64	      (if z
65		  (push  (list (* x y) x y) p)))
66	     )
67    p)
68  )
69(setq pals (palindrome-find))
70
71(sort pals (lambda (a b) (> (car a) (car b))))
72
73;;1st element is (906609 913 993)! so it works, but im not sure why my initial optimization failed
74;;this one is pretty fast though

DONE 5: Smallest multiple FF

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

A

 1(defun check-20 (x)
 2  (cl-loop for y from 1 to 20
 3	   for z = (= 0 (% x y))
 4	   until (not z)
 5	   finally return z))
 6
 7;;naive, but okay
 8(cl-loop for x from 20 to 2327925600 by 20
 9	 until (check-20 x)
10	 finally return x
11	 )
12232792560

DONE 6: Sum square difference

The sum of the squares of the first ten natural numbers is,

1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)^2 = 552 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

A

1(-  (expt (cl-loop for x from 1 to 100
2		   sum x) 2)
3    (cl-loop for x from 1 to 100
4	     sum (* x x)))
525164150

DONE 7: 10001st prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

A

1;; theres some offby 1 issues that i dont like, but this works and is unexpectedly fast
2(let ((primes 1)) (cl-loop for x from 2 to 200000
3			   until (= primes 10001)
4			   do (if (primep x ) (setq primes (1+ primes)))
5			   finally return (list primes (1- x))))

DONE 8: Largest product in a series FF

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

A

 1
 2(setq 1000-digits
 3'(
 4 7 3 1 6 7 1 7 6 5 3 1 3 3 0 6 2 4 9 1 9 2 2 5 1 1 9 6 7 4 4 2 6 5 7 4 7 4 2 3 5 5 3 4 9 1 9 4 9 3 4
 5 9 6 9 8 3 5 2 0 3 1 2 7 7 4 5 0 6 3 2 6 2 3 9 5 7 8 3 1 8 0 1 6 9 8 4 8 0 1 8 6 9 4 7 8 8 5 1 8 4 3
 6 8 5 8 6 1 5 6 0 7 8 9 1 1 2 9 4 9 4 9 5 4 5 9 5 0 1 7 3 7 9 5 8 3 3 1 9 5 2 8 5 3 2 0 8 8 0 5 5 1 1
 7 1 2 5 4 0 6 9 8 7 4 7 1 5 8 5 2 3 8 6 3 0 5 0 7 1 5 6 9 3 2 9 0 9 6 3 2 9 5 2 2 7 4 4 3 0 4 3 5 5 7
 8 6 6 8 9 6 6 4 8 9 5 0 4 4 5 2 4 4 5 2 3 1 6 1 7 3 1 8 5 6 4 0 3 0 9 8 7 1 1 1 2 1 7 2 2 3 8 3 1 1 3
 9 6 2 2 2 9 8 9 3 4 2 3 3 8 0 3 0 8 1 3 5 3 3 6 2 7 6 6 1 4 2 8 2 8 0 6 4 4 4 4 8 6 6 4 5 2 3 8 7 4 9
10 3 0 3 5 8 9 0 7 2 9 6 2 9 0 4 9 1 5 6 0 4 4 0 7 7 2 3 9 0 7 1 3 8 1 0 5 1 5 8 5 9 3 0 7 9 6 0 8 6 6
11 7 0 1 7 2 4 2 7 1 2 1 8 8 3 9 9 8 7 9 7 9 0 8 7 9 2 2 7 4 9 2 1 9 0 1 6 9 9 7 2 0 8 8 8 0 9 3 7 7 6
12 6 5 7 2 7 3 3 3 0 0 1 0 5 3 3 6 7 8 8 1 2 2 0 2 3 5 4 2 1 8 0 9 7 5 1 2 5 4 5 4 0 5 9 4 7 5 2 2 4 3
13 5 2 5 8 4 9 0 7 7 1 1 6 7 0 5 5 6 0 1 3 6 0 4 8 3 9 5 8 6 4 4 6 7 0 6 3 2 4 4 1 5 7 2 2 1 5 5 3 9 7
14 5 3 6 9 7 8 1 7 9 7 7 8 4 6 1 7 4 0 6 4 9 5 5 1 4 9 2 9 0 8 6 2 5 6 9 3 2 1 9 7 8 4 6 8 6 2 2 4 8 2
15 8 3 9 7 2 2 4 1 3 7 5 6 5 7 0 5 6 0 5 7 4 9 0 2 6 1 4 0 7 9 7 2 9 6 8 6 5 2 4 1 4 5 3 5 1 0 0 4 7 4
16 8 2 1 6 6 3 7 0 4 8 4 4 0 3 1 9 9 8 9 0 0 0 8 8 9 5 2 4 3 4 5 0 6 5 8 5 4 1 2 2 7 5 8 8 6 6 6 8 8 1
17 1 6 4 2 7 1 7 1 4 7 9 9 2 4 4 4 2 9 2 8 2 3 0 8 6 3 4 6 5 6 7 4 8 1 3 9 1 9 1 2 3 1 6 2 8 2 4 5 8 6
18 1 7 8 6 6 4 5 8 3 5 9 1 2 4 5 6 6 5 2 9 4 7 6 5 4 5 6 8 2 8 4 8 9 1 2 8 8 3 1 4 2 6 0 7 6 9 0 0 4 2
19 2 4 2 1 9 0 2 2 6 7 1 0 5 5 6 2 6 3 2 1 1 1 1 1 0 9 3 7 0 5 4 4 2 1 7 5 0 6 9 4 1 6 5 8 9 6 0 4 0 8
20 0 7 1 9 8 4 0 3 8 5 0 9 6 2 4 5 5 4 4 4 3 6 2 9 8 1 2 3 0 9 8 7 8 7 9 9 2 7 2 4 4 2 8 4 9 0 9 1 8 8
21 8 4 5 8 0 1 5 6 1 6 6 0 9 7 9 1 9 1 3 3 8 7 5 4 9 9 2 0 0 5 2 4 0 6 3 6 8 9 9 1 2 5 6 0 7 1 7 6 0 6
22 0 5 8 8 6 1 1 6 4 6 7 1 0 9 4 0 5 0 7 7 5 4 1 0 0 2 2 5 6 9 8 3 1 5 5 2 0 0 0 5 5 9 3 5 7 2 9 7 2 5
23 7 1 6 3 6 2 6 9 5 6 1 8 8 2 6 7 0 4 2 8 2 5 2 4 8 3 6 0 0 8 2 3 2 5 7 5 3 0 4 2 0 7 5 2 9 6 3 4 5 0
24))
25
26(defun 5-mult (digits index)
27  (* (nth index digits)
28     (nth (+ index 1)  digits)
29     (nth (+ index 2)  digits)
30     (nth (+ index 3)  digits)
31     (nth (+ index 4)  digits)))
32
33(cl-loop for i from 0 to 995
34	 maximize (5-mult 1000-digits i))

DONE 9: Special Pythagorean triplet USTT

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

A

http://en.wikipedia.org/wiki/Pythagorean_triple

Euclid's formula a=m^2-n^2 b=2mn c=m^2+n^2

a+b+c = m^2 - n^2 + 2mn + m^2 + n^2 = 1000 a+b+c = 2m^2 + 2mn = 1000 a+b+c = 2m(m + n) = 1000

abc = (m^2-n^2)2mn(m^2+n^2) = (m+n)(m-n)2mn = 1000n(m-n)

but its not obviously better than: a+b+c=1000 c=1000-b-c loop a b, terminate on a^2+b^2=c^2 to minimize looping, use a<b<c

 1(let ((sum 1000))
 2  (cl-loop
 3   for a from 1 to (/ sum 3)
 4   for abc =
 5   (cl-loop for b from a to (/ sum 2)
 6	    for c = (- sum a b)
 7	    for pythagorean = (= (+  (expt a 2) (expt b 2))   (expt c 2))
 8	    until pythagorean
 9	    finally return
10	    (if pythagorean (list a b c (+  (expt a 2) (expt b 2)) (expt c 2)  (* a b c) ))
11	    )
12   until abc
13   finally return abc))
14
15;;31875000

I'm not pleased with this solution, it should be possible to search with one variable.

DONE 10: Summation of primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

A

1
2  (let ((primesum 1))
3    (cl-loop for x from 2 to 20000000
4	     for isprime = (primep x)
5	     until (and isprime (> x  2000000))
6	     do (if isprime (setq primesum (+ primesum x)))
7	     finally return (list primesum x)))
8(142913828921 2000003)

DONE 11: Largest product in a grid

In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

 1
 2  (setq pe-11-grid
 3	'(
 4	     (08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08)
 5	     (49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00)
 6	     (81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65)
 7	     (52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91)
 8	     (22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80)
 9	     (24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50)
10	     (32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70)
11	     (67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21)
12	     (24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72)
13	     (21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95)
14	     (78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92)
15	     (16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57)
16	     (86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58)
17	     (19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40)
18	     (04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66)
19	     (88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69)
20	     (04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36)
21	     (20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16)
22	     (20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54)
23	     (01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48)
24	     ))
25
26(nth 1(nth 1 pe-11-grid ))
27
28(defun pe-grid-slice (grid x y length direction)
29  (let (( xinc 0) ( yinc 0) (rv))
30    (cond ((eq 'S direction) (setq yinc 1))
31	  ((eq 'E direction) (setq xinc 1))
32	  ((eq 'SE direction) (setq xinc 1)(setq yinc 1))
33	  ((eq 'SW direction) (setq xinc -1)(setq yinc 1))
34	  )
35    (cl-loop for i from 1 to length do
36	     (setq rv (cons (nth x (nth y grid)) rv)
37		   x (+ x xinc)
38		   y (+ y yinc)))
39    rv))
40
41(pe-grid-slice pe-11-grid 0 0 4 'S)
42(pe-grid-slice pe-11-grid 0 16 4 'S)
43(pe-grid-slice pe-11-grid 0 19 4 'E)
44(pe-grid-slice pe-11-grid 16 19 4 'E)
45(pe-grid-slice pe-11-grid 16 16 4 'SE)
46(apply '+ (pe-grid-slice pe-11-grid 0 0 4 'SE))
47
48(defun pe-11 ()
49  (max
50   ;; horizontal slices
51   (cl-loop for i from 0 to 16
52	    maximize (cl-loop for j from 0 to 19
53		     maximize (apply '* (pe-grid-slice pe-11-grid i j 4 'E))
54		     ))
55   ;; vertical slices
56   (cl-loop for i from 0 to 19
57	    maximize (cl-loop for j from 0 to 16
58		     maximize (apply '* (pe-grid-slice pe-11-grid i j 4 'S))
59		     ))
60   ;; SE slices
61   (cl-loop for i from 0 to 16
62	    maximize (cl-loop for j from 0 to 16
63		     maximize (apply '* (pe-grid-slice pe-11-grid i j 4 'SE))
64		     ))
65   ;; SW slices
66   (cl-loop for i from 3 to 19
67	    maximize (cl-loop for j from 0 to 16
68		     maximize (apply '* (pe-grid-slice pe-11-grid i j 4 'SW))
69		     )))
70  )
71(pe-11)

DONE 12: Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

 1 (defun pe-divisors (x)
 2  (remove nil (append (list 1 x) (cl-loop for i from 2 to (/ x 2)
 3					  collect (if (= 0 (% x i)) i)))))
 4
 5(defun pe-num-divisors (x)
 6  (let ((divisors 0))
 7    (cl-loop for i from 2 to (/ x 2)
 8	     do (if (= 0 (% x i)) (setq divisors (1+ divisors))))
 9    (+ 2 divisors)))
10
11;;this is optimized a bit by noticing factors are pairs, so loop to the square root, mult by 2
12;;(there might be some edge case unhandled)
13(defun pe-num-divisors-2 (x)
14  (let ((divisors 1))
15    (cl-loop for i from 2 to (sqrt x)
16	     do (if (= 0 (% x i)) (setq divisors (1+ divisors))))
17    (* 2 divisors)))
18
19
20(pe-divisors 15)
21(pe-num-divisors 15)
22(pe-num-divisors-2 15)
23(pe-divisors 28)
24
25(defun pe-12 (max)
26  (let ((acc 0) divs) (cl-loop for i from 1 to max do
27			       (setq acc (+ acc i))
28			       (setq divs (pe-divisors acc))
29			       collect (list acc (length divs) ;;divs
30					     ))))
31;;too slow with pe-num-divisors
32(defun pe-12-2 (max)
33  (let ((acc 0) divs) (cl-loop for i from 1 to max do
34			       (setq acc (+ acc i))
35			       (setq num-divs (pe-num-divisors-2 acc))
36			       collect (list acc  num-divs ;;divs
37					     ))))
38;; see http://en.wikipedia.org/wiki/Integer_factorization
39;;http://en.wikipedia.org/wiki/Trial_division
40
41;;som trial and terror yields
42;;(i like the trial so i can get a feel for what happens, which is the entire point)
43(pe-12-2 15000)
44...
45 (76576500 576)

DONE 13: Large sum FF

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.

37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 89261670696623633820136378418383684178734361726757 28112879812849979408065481931592621691275889832738 44274228917432520321923589422876796487670272189318 47451445736001306439091167216856844588711603153276 70386486105843025439939619828917593665686757934951 62176457141856560629502157223196586755079324193331 64906352462741904929101432445813822663347944758178 92575867718337217661963751590579239728245598838407 58203565325359399008402633568948830189458628227828 80181199384826282014278194139940567587151170094390 35398664372827112653829987240784473053190104293586 86515506006295864861532075273371959191420517255829 71693888707715466499115593487603532921714970056938 54370070576826684624621495650076471787294438377604 53282654108756828443191190634694037855217779295145 36123272525000296071075082563815656710885258350721 45876576172410976447339110607218265236877223636045 17423706905851860660448207621209813287860733969412 81142660418086830619328460811191061556940512689692 51934325451728388641918047049293215058642563049483 62467221648435076201727918039944693004732956340691 15732444386908125794514089057706229429197107928209 55037687525678773091862540744969844508330393682126 18336384825330154686196124348767681297534375946515 80386287592878490201521685554828717201219257766954 78182833757993103614740356856449095527097864797581 16726320100436897842553539920931837441497806860984 48403098129077791799088218795327364475675590848030 87086987551392711854517078544161852424320693150332 59959406895756536782107074926966537676326235447210 69793950679652694742597709739166693763042633987085 41052684708299085211399427365734116182760315001271 65378607361501080857009149939512557028198746004375 35829035317434717326932123578154982629742552737307 94953759765105305946966067683156574377167401875275 88902802571733229619176668713819931811048770190271 25267680276078003013678680992525463401061632866526 36270218540497705585629946580636237993140746255962 24074486908231174977792365466257246923322810917141 91430288197103288597806669760892938638285025333403 34413065578016127815921815005561868836468420090470 23053081172816430487623791969842487255036638784583 11487696932154902810424020138335124462181441773470 63783299490636259666498587618221225225512486764533 67720186971698544312419572409913959008952310058822 95548255300263520781532296796249481641953868218774 76085327132285723110424803456124867697064507995236 37774242535411291684276865538926205024910326572967 23701913275725675285653248258265463092207058596522 29798860272258331913126375147341994889534765745501 18495701454879288984856827726077713721403798879715 38298203783031473527721580348144513491373226651381 34829543829199918180278916522431027392251122869539 40957953066405232632538044100059654939159879593635 29746152185502371307642255121183693803580388584903 41698116222072977186158236678424689157993532961922 62467957194401269043877107275048102390895523597457 23189706772547915061505504953922979530901129967519 86188088225875314529584099251203829009407770775672 11306739708304724483816533873502340845647058077308 82959174767140363198008187129011875491310547126581 97623331044818386269515456334926366572897563400500 42846280183517070527831839425882145521227251250327 55121603546981200581762165212827652751691296897789 32238195734329339946437501907836945765883352399886 75506164965184775180738168837861091527357929701337 62177842752192623401942399639168044983993173312731 32924185707147349566916674687634660915035914677504 99518671430235219628894890102423325116913619626622 73267460800591547471830798392868535206946944540724 76841822524674417161514036427982273348055556214818 97142617910342598647204516893989422179826088076852 87783646182799346313767754307809363333018982642090 10848802521674670883215120185883543223812876952786 71329612474782464538636993009049310363619763878039 62184073572399794223406235393808339651327408011116 66627891981488087797941876876144230030984490851411 60661826293682836764744779239180335110989069790714 85786944089552990653640447425576083659976645795096 66024396409905389607120198219976047599490197230297 64913982680032973156037120041377903785566085089252 16730939319872750275468906903707539413042652315011 94809377245048795150954100921645863754710598436791 78639167021187492431995700641917969777599028300699 15368713711936614952811305876380278410754449733078 40789923115535562561142322423255033685442488917353 44889911501440648020369068063960672322193204149535 41503128880339536053299340368006977710650566631954 81234880673210146739058568557934581403627822703280 82616570773948327592232845941706525094512325230608 22918802058777319719839450180888072429661980811197 77158542502016545090413245809786882778948721859617 72107838435069186155435662884062257473692284509516 20849603980134001723930671666823555245252804609722 53503534226472524250874054075591789781264330331690

A

I simply added the numbers in emacs calc, which was easy but i only learned calc has bignums and is awesome.

DONE 14: Longest Collatz sequence PI

The following iterative sequence is defined for the set of positive integers:

n → n/2 (n is even) n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one million.

A

 1(defun collatz (start &optional cutoff)
 2    "return collatz sequence from START, stop when CUTOFF length is reached"
 3    (unless cutoff (setq cutoff 10000000))
 4    (cons start  (let ((n start) (n2))
 5		   (cl-loop for i from 1 to cutoff
 6			    do (if (oddp n)
 7				   (setq n2 (1+ (* 3 n )))
 8				 (setq n2 (/ n 2 )))
 9			    (setq n n2 )
10			    collect n
11
12			    until  (= n 1)))))
13(defun collatz-length (start &optional cutoff)
14    (unless cutoff (setq cutoff 10000000))
15    (let ((n start) (n2))
16      (cl-loop for i from 1 to cutoff
17	       do (if (oddp n)
18		      (setq n2 (1+ (* 3 n )))
19		    (setq n2 (/ n 2 )))
20	       (setq n n2 )
21	       ;;collect n
22
23	       until  (= n 1)
24	       finally return (1+ i))))
25
26
27  (length (collatz 13))
28  10
29(collatz-length 13)
30
31;;this is too slow
32(cl-loop for i from 1 to 1000000
33	 collect (list i (collatz-length i)))
34;;ideas:
35;; - some collatz contain others
36
37;;otoh it works, and after you sort the list you get max  (837799 525) which is correct

DONE 15: Lattice paths PI

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20×20 grid?

A

needed some hints for this one: http://en.wikipedia.org/wiki/Pascal%27s_triangle, see "Pascal's triangle overlaid on a grid"

 1  (defun pe-lattice-paths (size)
 2    (let ( (matrix))
 3      (cl-loop for i from 1 to size do (setq matrix (vconcat matrix (make-vector 1(make-vector size 1)) )))
 4
 5      (cl-loop for x from 1 to (1- size) do
 6	       (cl-loop for y from 1 to (1- size) do
 7			(aset (aref  matrix y) x
 8			      (+ (aref (aref matrix  y) (1- x))
 9				 (aref (aref matrix (1- y))  x)))
10	       ))
11
12      matrix)
13
14    )
15  (pe-lattice-paths 21)
16[[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
17 [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21]
18 [1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231]
19 [1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771]
20 [1 5 15 35 70 126 210 330 495 715 1001 1365 1820 2380 3060 3876 4845 5985 7315 8855 10626]
21 [1 6 21 56 126 252 462 792 1287 2002 3003 4368 6188 8568 11628 15504 20349 26334 33649 42504 53130]
22 [1 7 28 84 210 462 924 1716 3003 5005 8008 12376 18564 27132 38760 54264 74613 100947 134596 177100 230230]
23 [1 8 36 120 330 792 1716 3432 6435 11440 19448 31824 50388 77520 116280 170544 245157 346104 480700 657800 888030]
24 [1 9 45 165 495 1287 3003 6435 12870 24310 43758 75582 125970 203490 319770 490314 735471 1081575 1562275 2220075 3108105]
25 [1 10 55 220 715 2002 5005 11440 24310 48620 92378 167960 293930 497420 817190 1307504 2042975 3124550 4686825 6906900 10015005]
26 [1 11 66 286 1001 3003 8008 19448 43758 92378 184756 352716 646646 1144066 1961256 3268760 5311735 8436285 13123110 20030010 30045015]
27 [1 12 78 364 1365 4368 12376 31824 75582 167960 352716 705432 1352078 2496144 4457400 7726160 13037895 21474180 34597290 54627300 84672315]
28 [1 13 91 455 1820 6188 18564 50388 125970 293930 646646 1352078 2704156 5200300 9657700 17383860 30421755 51895935 86493225 141120525 225792840]
29 [1 14 105 560 2380 8568 27132 77520 203490 497420 1144066 2496144 5200300 10400600 20058300 37442160 67863915 119759850 206253075 347373600 573166440]
30 [1 15 120 680 3060 11628 38760 116280 319770 817190 1961256 4457400 9657700 20058300 40116600 77558760 145422675 265182525 471435600 818809200 1391975640]
31 [1 16 136 816 3876 15504 54264 170544 490314 1307504 3268760 7726160 17383860 37442160 77558760 155117520 300540195 565722720 1037158320 1855967520 3247943160]
32 [1 17 153 969 4845 20349 74613 245157 735471 2042975 5311735 13037895 30421755 67863915 145422675 300540195 601080390 1166803110 2203961430 4059928950 7307872110]
33 [1 18 171 1140 5985 26334 100947 346104 1081575 3124550 8436285 21474180 51895935 119759850 265182525 565722720 1166803110 2333606220 4537567650 8597496600 15905368710]
34 [1 19 190 1330 7315 33649 134596 480700 1562275 4686825 13123110 34597290 86493225 206253075 471435600 1037158320 2203961430 4537567650 9075135300 17672631900 33578000610]
35 [1 20 210 1540 8855 42504 177100 657800 2220075 6906900 20030010 54627300 141120525 347373600 818809200 1855967520 4059928950 8597496600 17672631900 35345263800 68923264410]
36 [1 21 231 1771 10626 53130 230230 888030 3108105 10015005 30045015 84672315 225792840 573166440 1391975640 3247943160 7307872110 15905368710 33578000610 68923264410 137846528820]]

DONE 16: Power digit sum US

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2^1000?

A

 1;;2^1000 as a string
 2(math-format-number (math-pow 2 1000))
 3"10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376"
 4
 5(string-to-number (substring (math-format-number (math-pow 2 1000)) 2 3))
 6
 7(defun power-digit-sum ()
 8  (let ((powstr (math-format-number (math-pow 2 1000))))
 9    (cl-loop for i from 0 to (1- (length powstr))
10	     sum (string-to-number (substring powstr i (1+ i)))
11	     )))
121366

DONE 17: Number letter counts

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.

A

have a look at (cl-format nil "~r" 342) "three hundred and forty-two" thats pretty nifty!

1
2
3(cl-loop for i from 1 to 1000  collect (cl-format nil "~r" i))
4(length (remove (string-to-char "-") (remove (string-to-char " ") "nine hundred and ninety-eight" )))
5
6(cl-loop for i from 1 to 1000  sum (length (remove (string-to-char "-") (remove (string-to-char " ") (cl-format nil "~r" i) )))
7)

DONE 18: Maximum path sum I

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3 7 4 2 4 6 8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

          75
         95 64
        17 47 82
       18 35 87 10
      20 04 82 47 65
     19 01 23 75 03 34
    88 02 77 73 07 63 67
   99 65 04 28 06 16 70 92
  41 41 26 56 83 40 80 70 33
 41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14

70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

A

seems similar to the pascal triangle problem. it should be possible to store the max sum from just the 2 neighbours in each cell, and move row by row until bottom. the sought max is then the max of the cells in the bottom row. this should be efficient enough also for problem 67!

 1
 2(setq pe-18-pyramid
 3      [
 4       [              75]
 5       [             95 64]
 6       [            17 47 82]
 7       [           18 35 87 10]
 8       [          20 04 82 47 65]
 9       [         19 01 23 75 03 34]
10       [        88 02 77 73 07 63 67]
11       [       99 65 04 28 06 16 70 92]
12       [      41 41 26 56 83 40 80 70 33]
13       [     41 48 72 33 47 32 37 16 94 29]
14       [    53 71 44 65 25 43 91 52 97 51 14]
15       [   70 11 33 28 77 73 17 78 39 68 17 57]
16       [  91 71 52 38 17 14 91 43 58 50 27 29 48]
17       [ 63 66 04 68 89 53 67 30 73 16 69 87 40 31]
18       [04 62 98 27 23 09 70 98 73 93 38 53 60 04 23]
19       ])
20(setq pe-18-test-pyramid
21      [
22       [ 3]
23       [ 7 4]
24       [ 2 4 6]
25       [ 8 5 9 3]])
26
27(defun aref-matrix (matrix x y) (aref (aref matrix  y)  x))
28(defun aset-matrix (matrix x y v) (aset (aref matrix y) x v))
29
30(defun pe-18-max-neighbour-sum (matrix x y)
31  (let ( (neighbour-NE (condition-case nil (aref-matrix matrix x (1- y) ) (error 0))         )
32	 (neighbour-NW (condition-case nil (aref-matrix matrix (1-  x) (1- y) ) (error 0)) ))
33    (max (+ ( aref-matrix matrix x y) neighbour-NW)
34	 (+ ( aref-matrix matrix x y) neighbour-NE)
35	 ))
36
37  )
38(defun pe-18-max-pyramid (matrix)
39  (cl-loop for y from 0 to (1- (length matrix)) do
40	   (cl-loop for x from 0 to y do
41		    (message "X %d Y %d v %d" x y (aref-matrix matrix x y))
42		    (aset-matrix matrix x y  (pe-18-max-neighbour-sum matrix x y))
43		    )
44	   )
45  matrix)
46
47(pe-18-max-pyramid (copy-tree  pe-18-test-pyramid t))
48[[3] [10 7] [12 14 13] [20 19 23 16]]
49
50(pe-18-max-pyramid (copy-tree  pe-18-pyramid t))
51[[75]
52 [170 139]
53 [187 217 221]
54 [205 252 308 231]
55 [225 256 390 355 296]
56 [244 257 413 465 358 330]
57 [332 259 490 538 472 421 397]
58 [431 397 494 566 544 488 491 489]
59 [472 472 520 622 649 584 571 561 522]
60 [513 520 592 655 696 681 621 587 655 551]
61 [566 591 636 720 721 739 772 673 752 706 565]
62 [636 602 669 748 798 812 789 850 791 820 723 622]
63 [727 707 721 786 815 826 903 893 908 870 847 752 670]
64 [790 793 725 854 904 879 970 933 981 924 939 934 792 701]
65 [794 855 891 881 927 913 1040 1068 1054 1074 977 992 994 796 724]]
66
67;;so max is 1074

DONE 19: Counting Sundays

You are given the following information, but you may prefer to do some research for yourself.

  • 1 Jan 1900 was a Monday.

Thirty days has September, April, June and November. All the rest have thirty-one, Saving February alone, Which has twenty-eight, rain or shine. And on leap years, twenty-nine.

  • A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

A

use the emacs calendar arithmetic perhaps?

1;;this returns a list of strings of dates
2(cl-loop for i from 1 to 1200 collect (format-time-string "%w    %Y %B %e %A" (encode-time 0 0 0 1 i 1901)))
3;;this counts the sundays
4(cl-loop for i from 1 to 1200 count (equal "0" (format-time-string "%w" (encode-time 0 0 0 1 i 1901))))
5171

DONE 20: Factorial digit sum

n! means n × (n − 1) × ... × 3 × 2 × 1

For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!

A

1(math-format-number (calcFunc-fact 100))
2"93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000"
3
4(digit-sum  (calcFunc-fact 100))
5648

DONE 21: Amicable numbers FF

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).

If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

A

 1(pe-divisors 220)
 2(- (+ 1 220 2 4 5 10 11 20 22 44 55 110) 220) 284
 3
 4(pe-divisors 284)
 5
 6(-(+ 1 284 2 4 71 142) 284) 220
 7
 8(defun pe-21-sum-divisors (n)
 9  (- (apply '+ (pe-divisors n)) n))
10
11(pe-21-sum-divisors 284) 220
12
13(defun pe-21-amicablep (n)
14  (let* ((a (pe-21-sum-divisors n))
15	(b (pe-21-sum-divisors a)))
16    (if (=  b n) (list  a b))))
17
18(pe-21-amicablep 220)
19
20(cl-loop for n from 1 to 10000
21	 for amicable = (pe-21-amicablep n)
22	 when amicable
23	 collect  amicable )
24
25((1 1)
26 (6 6)
27 (28 28)
28 (284 220)
29 (220 284)
30 (496 496)
31 (1210 1184)
32 (1184 1210)
33 (2924 2620)
34 (2620 2924)
35 (5564 5020)
36 (5020 5564)
37 (6368 6232)
38 (6232 6368)
39 (8128 8128))
40
41;filter away the stuff that arent unique pairs
42(+  284 220  1210 1184 2924 2620 5564 5020 6368 6232 )
4331626
44;my solution is so far buggy and slow but it works to a degree

DONE 22: Names scores

Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.

For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 × 53 = 49714.

What is the total of all the name scores in the file?

A

   1(setq pe-22-names '(
   2"MARY"
   3"PATRICIA"
   4"LINDA"
   5"BARBARA"
   6"ELIZABETH"
   7"JENNIFER"
   8"MARIA"
   9"SUSAN"
  10"MARGARET"
  11"DOROTHY"
  12"LISA"
  13"NANCY"
  14"KAREN"
  15"BETTY"
  16"HELEN"
  17"SANDRA"
  18"DONNA"
  19"CAROL"
  20"RUTH"
  21"SHARON"
  22"MICHELLE"
  23"LAURA"
  24"SARAH"
  25"KIMBERLY"
  26"DEBORAH"
  27"JESSICA"
  28"SHIRLEY"
  29"CYNTHIA"
  30"ANGELA"
  31"MELISSA"
  32"BRENDA"
  33"AMY"
  34"ANNA"
  35"REBECCA"
  36"VIRGINIA"
  37"KATHLEEN"
  38"PAMELA"
  39"MARTHA"
  40"DEBRA"
  41"AMANDA"
  42"STEPHANIE"
  43"CAROLYN"
  44"CHRISTINE"
  45"MARIE"
  46"JANET"
  47"CATHERINE"
  48"FRANCES"
  49"ANN"
  50"JOYCE"
  51"DIANE"
  52"ALICE"
  53"JULIE"
  54"HEATHER"
  55"TERESA"
  56"DORIS"
  57"GLORIA"
  58"EVELYN"
  59"JEAN"
  60"CHERYL"
  61"MILDRED"
  62"KATHERINE"
  63"JOAN"
  64"ASHLEY"
  65"JUDITH"
  66"ROSE"
  67"JANICE"
  68"KELLY"
  69"NICOLE"
  70"JUDY"
  71"CHRISTINA"
  72"KATHY"
  73"THERESA"
  74"BEVERLY"
  75"DENISE"
  76"TAMMY"
  77"IRENE"
  78"JANE"
  79"LORI"
  80"RACHEL"
  81"MARILYN"
  82"ANDREA"
  83"KATHRYN"
  84"LOUISE"
  85"SARA"
  86"ANNE"
  87"JACQUELINE"
  88"WANDA"
  89"BONNIE"
  90"JULIA"
  91"RUBY"
  92"LOIS"
  93"TINA"
  94"PHYLLIS"
  95"NORMA"
  96"PAULA"
  97"DIANA"
  98"ANNIE"
  99"LILLIAN"
 100"EMILY"
 101"ROBIN"
 102"PEGGY"
 103"CRYSTAL"
 104"GLADYS"
 105"RITA"
 106"DAWN"
 107"CONNIE"
 108"FLORENCE"
 109"TRACY"
 110"EDNA"
 111"TIFFANY"
 112"CARMEN"
 113"ROSA"
 114"CINDY"
 115"GRACE"
 116"WENDY"
 117"VICTORIA"
 118"EDITH"
 119"KIM"
 120"SHERRY"
 121"SYLVIA"
 122"JOSEPHINE"
 123"THELMA"
 124"SHANNON"
 125"SHEILA"
 126"ETHEL"
 127"ELLEN"
 128"ELAINE"
 129"MARJORIE"
 130"CARRIE"
 131"CHARLOTTE"
 132"MONICA"
 133"ESTHER"
 134"PAULINE"
 135"EMMA"
 136"JUANITA"
 137"ANITA"
 138"RHONDA"
 139"HAZEL"
 140"AMBER"
 141"EVA"
 142"DEBBIE"
 143"APRIL"
 144"LESLIE"
 145"CLARA"
 146"LUCILLE"
 147"JAMIE"
 148"JOANNE"
 149"ELEANOR"
 150"VALERIE"
 151"DANIELLE"
 152"MEGAN"
 153"ALICIA"
 154"SUZANNE"
 155"MICHELE"
 156"GAIL"
 157"BERTHA"
 158"DARLENE"
 159"VERONICA"
 160"JILL"
 161"ERIN"
 162"GERALDINE"
 163"LAUREN"
 164"CATHY"
 165"JOANN"
 166"LORRAINE"
 167"LYNN"
 168"SALLY"
 169"REGINA"
 170"ERICA"
 171"BEATRICE"
 172"DOLORES"
 173"BERNICE"
 174"AUDREY"
 175"YVONNE"
 176"ANNETTE"
 177"JUNE"
 178"SAMANTHA"
 179"MARION"
 180"DANA"
 181"STACY"
 182"ANA"
 183"RENEE"
 184"IDA"
 185"VIVIAN"
 186"ROBERTA"
 187"HOLLY"
 188"BRITTANY"
 189"MELANIE"
 190"LORETTA"
 191"YOLANDA"
 192"JEANETTE"
 193"LAURIE"
 194"KATIE"
 195"KRISTEN"
 196"VANESSA"
 197"ALMA"
 198"SUE"
 199"ELSIE"
 200"BETH"
 201"JEANNE"
 202"VICKI"
 203"CARLA"
 204"TARA"
 205"ROSEMARY"
 206"EILEEN"
 207"TERRI"
 208"GERTRUDE"
 209"LUCY"
 210"TONYA"
 211"ELLA"
 212"STACEY"
 213"WILMA"
 214"GINA"
 215"KRISTIN"
 216"JESSIE"
 217"NATALIE"
 218"AGNES"
 219"VERA"
 220"WILLIE"
 221"CHARLENE"
 222"BESSIE"
 223"DELORES"
 224"MELINDA"
 225"PEARL"
 226"ARLENE"
 227"MAUREEN"
 228"COLLEEN"
 229"ALLISON"
 230"TAMARA"
 231"JOY"
 232"GEORGIA"
 233"CONSTANCE"
 234"LILLIE"
 235"CLAUDIA"
 236"JACKIE"
 237"MARCIA"
 238"TANYA"
 239"NELLIE"
 240"MINNIE"
 241"MARLENE"
 242"HEIDI"
 243"GLENDA"
 244"LYDIA"
 245"VIOLA"
 246"COURTNEY"
 247"MARIAN"
 248"STELLA"
 249"CAROLINE"
 250"DORA"
 251"JO"
 252"VICKIE"
 253"MATTIE"
 254"TERRY"
 255"MAXINE"
 256"IRMA"
 257"MABEL"
 258"MARSHA"
 259"MYRTLE"
 260"LENA"
 261"CHRISTY"
 262"DEANNA"
 263"PATSY"
 264"HILDA"
 265"GWENDOLYN"
 266"JENNIE"
 267"NORA"
 268"MARGIE"
 269"NINA"
 270"CASSANDRA"
 271"LEAH"
 272"PENNY"
 273"KAY"
 274"PRISCILLA"
 275"NAOMI"
 276"CAROLE"
 277"BRANDY"
 278"OLGA"
 279"BILLIE"
 280"DIANNE"
 281"TRACEY"
 282"LEONA"
 283"JENNY"
 284"FELICIA"
 285"SONIA"
 286"MIRIAM"
 287"VELMA"
 288"BECKY"
 289"BOBBIE"
 290"VIOLET"
 291"KRISTINA"
 292"TONI"
 293"MISTY"
 294"MAE"
 295"SHELLY"
 296"DAISY"
 297"RAMONA"
 298"SHERRI"
 299"ERIKA"
 300"KATRINA"
 301"CLAIRE"
 302"LINDSEY"
 303"LINDSAY"
 304"GENEVA"
 305"GUADALUPE"
 306"BELINDA"
 307"MARGARITA"
 308"SHERYL"
 309"CORA"
 310"FAYE"
 311"ADA"
 312"NATASHA"
 313"SABRINA"
 314"ISABEL"
 315"MARGUERITE"
 316"HATTIE"
 317"HARRIET"
 318"MOLLY"
 319"CECILIA"
 320"KRISTI"
 321"BRANDI"
 322"BLANCHE"
 323"SANDY"
 324"ROSIE"
 325"JOANNA"
 326"IRIS"
 327"EUNICE"
 328"ANGIE"
 329"INEZ"
 330"LYNDA"
 331"MADELINE"
 332"AMELIA"
 333"ALBERTA"
 334"GENEVIEVE"
 335"MONIQUE"
 336"JODI"
 337"JANIE"
 338"MAGGIE"
 339"KAYLA"
 340"SONYA"
 341"JAN"
 342"LEE"
 343"KRISTINE"
 344"CANDACE"
 345"FANNIE"
 346"MARYANN"
 347"OPAL"
 348"ALISON"
 349"YVETTE"
 350"MELODY"
 351"LUZ"
 352"SUSIE"
 353"OLIVIA"
 354"FLORA"
 355"SHELLEY"
 356"KRISTY"
 357"MAMIE"
 358"LULA"
 359"LOLA"
 360"VERNA"
 361"BEULAH"
 362"ANTOINETTE"
 363"CANDICE"
 364"JUANA"
 365"JEANNETTE"
 366"PAM"
 367"KELLI"
 368"HANNAH"
 369"WHITNEY"
 370"BRIDGET"
 371"KARLA"
 372"CELIA"
 373"LATOYA"
 374"PATTY"
 375"SHELIA"
 376"GAYLE"
 377"DELLA"
 378"VICKY"
 379"LYNNE"
 380"SHERI"
 381"MARIANNE"
 382"KARA"
 383"JACQUELYN"
 384"ERMA"
 385"BLANCA"
 386"MYRA"
 387"LETICIA"
 388"PAT"
 389"KRISTA"
 390"ROXANNE"
 391"ANGELICA"
 392"JOHNNIE"
 393"ROBYN"
 394"FRANCIS"
 395"ADRIENNE"
 396"ROSALIE"
 397"ALEXANDRA"
 398"BROOKE"
 399"BETHANY"
 400"SADIE"
 401"BERNADETTE"
 402"TRACI"
 403"JODY"
 404"KENDRA"
 405"JASMINE"
 406"NICHOLE"
 407"RACHAEL"
 408"CHELSEA"
 409"MABLE"
 410"ERNESTINE"
 411"MURIEL"
 412"MARCELLA"
 413"ELENA"
 414"KRYSTAL"
 415"ANGELINA"
 416"NADINE"
 417"KARI"
 418"ESTELLE"
 419"DIANNA"
 420"PAULETTE"
 421"LORA"
 422"MONA"
 423"DOREEN"
 424"ROSEMARIE"
 425"ANGEL"
 426"DESIREE"
 427"ANTONIA"
 428"HOPE"
 429"GINGER"
 430"JANIS"
 431"BETSY"
 432"CHRISTIE"
 433"FREDA"
 434"MERCEDES"
 435"MEREDITH"
 436"LYNETTE"
 437"TERI"
 438"CRISTINA"
 439"EULA"
 440"LEIGH"
 441"MEGHAN"
 442"SOPHIA"
 443"ELOISE"
 444"ROCHELLE"
 445"GRETCHEN"
 446"CECELIA"
 447"RAQUEL"
 448"HENRIETTA"
 449"ALYSSA"
 450"JANA"
 451"KELLEY"
 452"GWEN"
 453"KERRY"
 454"JENNA"
 455"TRICIA"
 456"LAVERNE"
 457"OLIVE"
 458"ALEXIS"
 459"TASHA"
 460"SILVIA"
 461"ELVIRA"
 462"CASEY"
 463"DELIA"
 464"SOPHIE"
 465"KATE"
 466"PATTI"
 467"LORENA"
 468"KELLIE"
 469"SONJA"
 470"LILA"
 471"LANA"
 472"DARLA"
 473"MAY"
 474"MINDY"
 475"ESSIE"
 476"MANDY"
 477"LORENE"
 478"ELSA"
 479"JOSEFINA"
 480"JEANNIE"
 481"MIRANDA"
 482"DIXIE"
 483"LUCIA"
 484"MARTA"
 485"FAITH"
 486"LELA"
 487"JOHANNA"
 488"SHARI"
 489"CAMILLE"
 490"TAMI"
 491"SHAWNA"
 492"ELISA"
 493"EBONY"
 494"MELBA"
 495"ORA"
 496"NETTIE"
 497"TABITHA"
 498"OLLIE"
 499"JAIME"
 500"WINIFRED"
 501"KRISTIE"
 502"MARINA"
 503"ALISHA"
 504"AIMEE"
 505"RENA"
 506"MYRNA"
 507"MARLA"
 508"TAMMIE"
 509"LATASHA"
 510"BONITA"
 511"PATRICE"
 512"RONDA"
 513"SHERRIE"
 514"ADDIE"
 515"FRANCINE"
 516"DELORIS"
 517"STACIE"
 518"ADRIANA"
 519"CHERI"
 520"SHELBY"
 521"ABIGAIL"
 522"CELESTE"
 523"JEWEL"
 524"CARA"
 525"ADELE"
 526"REBEKAH"
 527"LUCINDA"
 528"DORTHY"
 529"CHRIS"
 530"EFFIE"
 531"TRINA"
 532"REBA"
 533"SHAWN"
 534"SALLIE"
 535"AURORA"
 536"LENORA"
 537"ETTA"
 538"LOTTIE"
 539"KERRI"
 540"TRISHA"
 541"NIKKI"
 542"ESTELLA"
 543"FRANCISCA"
 544"JOSIE"
 545"TRACIE"
 546"MARISSA"
 547"KARIN"
 548"BRITTNEY"
 549"JANELLE"
 550"LOURDES"
 551"LAUREL"
 552"HELENE"
 553"FERN"
 554"ELVA"
 555"CORINNE"
 556"KELSEY"
 557"INA"
 558"BETTIE"
 559"ELISABETH"
 560"AIDA"
 561"CAITLIN"
 562"INGRID"
 563"IVA"
 564"EUGENIA"
 565"CHRISTA"
 566"GOLDIE"
 567"CASSIE"
 568"MAUDE"
 569"JENIFER"
 570"THERESE"
 571"FRANKIE"
 572"DENA"
 573"LORNA"
 574"JANETTE"
 575"LATONYA"
 576"CANDY"
 577"MORGAN"
 578"CONSUELO"
 579"TAMIKA"
 580"ROSETTA"
 581"DEBORA"
 582"CHERIE"
 583"POLLY"
 584"DINA"
 585"JEWELL"
 586"FAY"
 587"JILLIAN"
 588"DOROTHEA"
 589"NELL"
 590"TRUDY"
 591"ESPERANZA"
 592"PATRICA"
 593"KIMBERLEY"
 594"SHANNA"
 595"HELENA"
 596"CAROLINA"
 597"CLEO"
 598"STEFANIE"
 599"ROSARIO"
 600"OLA"
 601"JANINE"
 602"MOLLIE"
 603"LUPE"
 604"ALISA"
 605"LOU"
 606"MARIBEL"
 607"SUSANNE"
 608"BETTE"
 609"SUSANA"
 610"ELISE"
 611"CECILE"
 612"ISABELLE"
 613"LESLEY"
 614"JOCELYN"
 615"PAIGE"
 616"JONI"
 617"RACHELLE"
 618"LEOLA"
 619"DAPHNE"
 620"ALTA"
 621"ESTER"
 622"PETRA"
 623"GRACIELA"
 624"IMOGENE"
 625"JOLENE"
 626"KEISHA"
 627"LACEY"
 628"GLENNA"
 629"GABRIELA"
 630"KERI"
 631"URSULA"
 632"LIZZIE"
 633"KIRSTEN"
 634"SHANA"
 635"ADELINE"
 636"MAYRA"
 637"JAYNE"
 638"JACLYN"
 639"GRACIE"
 640"SONDRA"
 641"CARMELA"
 642"MARISA"
 643"ROSALIND"
 644"CHARITY"
 645"TONIA"
 646"BEATRIZ"
 647"MARISOL"
 648"CLARICE"
 649"JEANINE"
 650"SHEENA"
 651"ANGELINE"
 652"FRIEDA"
 653"LILY"
 654"ROBBIE"
 655"SHAUNA"
 656"MILLIE"
 657"CLAUDETTE"
 658"CATHLEEN"
 659"ANGELIA"
 660"GABRIELLE"
 661"AUTUMN"
 662"KATHARINE"
 663"SUMMER"
 664"JODIE"
 665"STACI"
 666"LEA"
 667"CHRISTI"
 668"JIMMIE"
 669"JUSTINE"
 670"ELMA"
 671"LUELLA"
 672"MARGRET"
 673"DOMINIQUE"
 674"SOCORRO"
 675"RENE"
 676"MARTINA"
 677"MARGO"
 678"MAVIS"
 679"CALLIE"
 680"BOBBI"
 681"MARITZA"
 682"LUCILE"
 683"LEANNE"
 684"JEANNINE"
 685"DEANA"
 686"AILEEN"
 687"LORIE"
 688"LADONNA"
 689"WILLA"
 690"MANUELA"
 691"GALE"
 692"SELMA"
 693"DOLLY"
 694"SYBIL"
 695"ABBY"
 696"LARA"
 697"DALE"
 698"IVY"
 699"DEE"
 700"WINNIE"
 701"MARCY"
 702"LUISA"
 703"JERI"
 704"MAGDALENA"
 705"OFELIA"
 706"MEAGAN"
 707"AUDRA"
 708"MATILDA"
 709"LEILA"
 710"CORNELIA"
 711"BIANCA"
 712"SIMONE"
 713"BETTYE"
 714"RANDI"
 715"VIRGIE"
 716"LATISHA"
 717"BARBRA"
 718"GEORGINA"
 719"ELIZA"
 720"LEANN"
 721"BRIDGETTE"
 722"RHODA"
 723"HALEY"
 724"ADELA"
 725"NOLA"
 726"BERNADINE"
 727"FLOSSIE"
 728"ILA"
 729"GRETA"
 730"RUTHIE"
 731"NELDA"
 732"MINERVA"
 733"LILLY"
 734"TERRIE"
 735"LETHA"
 736"HILARY"
 737"ESTELA"
 738"VALARIE"
 739"BRIANNA"
 740"ROSALYN"
 741"EARLINE"
 742"CATALINA"
 743"AVA"
 744"MIA"
 745"CLARISSA"
 746"LIDIA"
 747"CORRINE"
 748"ALEXANDRIA"
 749"CONCEPCION"
 750"TIA"
 751"SHARRON"
 752"RAE"
 753"DONA"
 754"ERICKA"
 755"JAMI"
 756"ELNORA"
 757"CHANDRA"
 758"LENORE"
 759"NEVA"
 760"MARYLOU"
 761"MELISA"
 762"TABATHA"
 763"SERENA"
 764"AVIS"
 765"ALLIE"
 766"SOFIA"
 767"JEANIE"
 768"ODESSA"
 769"NANNIE"
 770"HARRIETT"
 771"LORAINE"
 772"PENELOPE"
 773"MILAGROS"
 774"EMILIA"
 775"BENITA"
 776"ALLYSON"
 777"ASHLEE"
 778"TANIA"
 779"TOMMIE"
 780"ESMERALDA"
 781"KARINA"
 782"EVE"
 783"PEARLIE"
 784"ZELMA"
 785"MALINDA"
 786"NOREEN"
 787"TAMEKA"
 788"SAUNDRA"
 789"HILLARY"
 790"AMIE"
 791"ALTHEA"
 792"ROSALINDA"
 793"JORDAN"
 794"LILIA"
 795"ALANA"
 796"GAY"
 797"CLARE"
 798"ALEJANDRA"
 799"ELINOR"
 800"MICHAEL"
 801"LORRIE"
 802"JERRI"
 803"DARCY"
 804"EARNESTINE"
 805"CARMELLA"
 806"TAYLOR"
 807"NOEMI"
 808"MARCIE"
 809"LIZA"
 810"ANNABELLE"
 811"LOUISA"
 812"EARLENE"
 813"MALLORY"
 814"CARLENE"
 815"NITA"
 816"SELENA"
 817"TANISHA"
 818"KATY"
 819"JULIANNE"
 820"JOHN"
 821"LAKISHA"
 822"EDWINA"
 823"MARICELA"
 824"MARGERY"
 825"KENYA"
 826"DOLLIE"
 827"ROXIE"
 828"ROSLYN"
 829"KATHRINE"
 830"NANETTE"
 831"CHARMAINE"
 832"LAVONNE"
 833"ILENE"
 834"KRIS"
 835"TAMMI"
 836"SUZETTE"
 837"CORINE"
 838"KAYE"
 839"JERRY"
 840"MERLE"
 841"CHRYSTAL"
 842"LINA"
 843"DEANNE"
 844"LILIAN"
 845"JULIANA"
 846"ALINE"
 847"LUANN"
 848"KASEY"
 849"MARYANNE"
 850"EVANGELINE"
 851"COLETTE"
 852"MELVA"
 853"LAWANDA"
 854"YESENIA"
 855"NADIA"
 856"MADGE"
 857"KATHIE"
 858"EDDIE"
 859"OPHELIA"
 860"VALERIA"
 861"NONA"
 862"MITZI"
 863"MARI"
 864"GEORGETTE"
 865"CLAUDINE"
 866"FRAN"
 867"ALISSA"
 868"ROSEANN"
 869"LAKEISHA"
 870"SUSANNA"
 871"REVA"
 872"DEIDRE"
 873"CHASITY"
 874"SHEREE"
 875"CARLY"
 876"JAMES"
 877"ELVIA"
 878"ALYCE"
 879"DEIRDRE"
 880"GENA"
 881"BRIANA"
 882"ARACELI"
 883"KATELYN"
 884"ROSANNE"
 885"WENDI"
 886"TESSA"
 887"BERTA"
 888"MARVA"
 889"IMELDA"
 890"MARIETTA"
 891"MARCI"
 892"LEONOR"
 893"ARLINE"
 894"SASHA"
 895"MADELYN"
 896"JANNA"
 897"JULIETTE"
 898"DEENA"
 899"AURELIA"
 900"JOSEFA"
 901"AUGUSTA"
 902"LILIANA"
 903"YOUNG"
 904"CHRISTIAN"
 905"LESSIE"
 906"AMALIA"
 907"SAVANNAH"
 908"ANASTASIA"
 909"VILMA"
 910"NATALIA"
 911"ROSELLA"
 912"LYNNETTE"
 913"CORINA"
 914"ALFREDA"
 915"LEANNA"
 916"CAREY"
 917"AMPARO"
 918"COLEEN"
 919"TAMRA"
 920"AISHA"
 921"WILDA"
 922"KARYN"
 923"CHERRY"
 924"QUEEN"
 925"MAURA"
 926"MAI"
 927"EVANGELINA"
 928"ROSANNA"
 929"HALLIE"
 930"ERNA"
 931"ENID"
 932"MARIANA"
 933"LACY"
 934"JULIET"
 935"JACKLYN"
 936"FREIDA"
 937"MADELEINE"
 938"MARA"
 939"HESTER"
 940"CATHRYN"
 941"LELIA"
 942"CASANDRA"
 943"BRIDGETT"
 944"ANGELITA"
 945"JANNIE"
 946"DIONNE"
 947"ANNMARIE"
 948"KATINA"
 949"BERYL"
 950"PHOEBE"
 951"MILLICENT"
 952"KATHERYN"
 953"DIANN"
 954"CARISSA"
 955"MARYELLEN"
 956"LIZ"
 957"LAURI"
 958"HELGA"
 959"GILDA"
 960"ADRIAN"
 961"RHEA"
 962"MARQUITA"
 963"HOLLIE"
 964"TISHA"
 965"TAMERA"
 966"ANGELIQUE"
 967"FRANCESCA"
 968"BRITNEY"
 969"KAITLIN"
 970"LOLITA"
 971"FLORINE"
 972"ROWENA"
 973"REYNA"
 974"TWILA"
 975"FANNY"
 976"JANELL"
 977"INES"
 978"CONCETTA"
 979"BERTIE"
 980"ALBA"
 981"BRIGITTE"
 982"ALYSON"
 983"VONDA"
 984"PANSY"
 985"ELBA"
 986"NOELLE"
 987"LETITIA"
 988"KITTY"
 989"DEANN"
 990"BRANDIE"
 991"LOUELLA"
 992"LETA"
 993"FELECIA"
 994"SHARLENE"
 995"LESA"
 996"BEVERLEY"
 997"ROBERT"
 998"ISABELLA"
 999"HERMINIA"
1000"TERRA"
1001"CELINA"
1002"TORI"
1003"OCTAVIA"
1004"JADE"
1005"DENICE"
1006"GERMAINE"
1007"SIERRA"
1008"MICHELL"
1009"CORTNEY"
1010"NELLY"
1011"DORETHA"
1012"SYDNEY"
1013"DEIDRA"
1014"MONIKA"
1015"LASHONDA"
1016"JUDI"
1017"CHELSEY"
1018"ANTIONETTE"
1019"MARGOT"
1020"BOBBY"
1021"ADELAIDE"
1022"NAN"
1023"LEEANN"
1024"ELISHA"
1025"DESSIE"
1026"LIBBY"
1027"KATHI"
1028"GAYLA"
1029"LATANYA"
1030"MINA"
1031"MELLISA"
1032"KIMBERLEE"
1033"JASMIN"
1034"RENAE"
1035"ZELDA"
1036"ELDA"
1037"MA"
1038"JUSTINA"
1039"GUSSIE"
1040"EMILIE"
1041"CAMILLA"
1042"ABBIE"
1043"ROCIO"
1044"KAITLYN"
1045"JESSE"
1046"EDYTHE"
1047"ASHLEIGH"
1048"SELINA"
1049"LAKESHA"
1050"GERI"
1051"ALLENE"
1052"PAMALA"
1053"MICHAELA"
1054"DAYNA"
1055"CARYN"
1056"ROSALIA"
1057"SUN"
1058"JACQULINE"
1059"REBECA"
1060"MARYBETH"
1061"KRYSTLE"
1062"IOLA"
1063"DOTTIE"
1064"BENNIE"
1065"BELLE"
1066"AUBREY"
1067"GRISELDA"
1068"ERNESTINA"
1069"ELIDA"
1070"ADRIANNE"
1071"DEMETRIA"
1072"DELMA"
1073"CHONG"
1074"JAQUELINE"
1075"DESTINY"
1076"ARLEEN"
1077"VIRGINA"
1078"RETHA"
1079"FATIMA"
1080"TILLIE"
1081"ELEANORE"
1082"CARI"
1083"TREVA"
1084"BIRDIE"
1085"WILHELMINA"
1086"ROSALEE"
1087"MAURINE"
1088"LATRICE"
1089"YONG"
1090"JENA"
1091"TARYN"
1092"ELIA"
1093"DEBBY"
1094"MAUDIE"
1095"JEANNA"
1096"DELILAH"
1097"CATRINA"
1098"SHONDA"
1099"HORTENCIA"
1100"THEODORA"
1101"TERESITA"
1102"ROBBIN"
1103"DANETTE"
1104"MARYJANE"
1105"FREDDIE"
1106"DELPHINE"
1107"BRIANNE"
1108"NILDA"
1109"DANNA"
1110"CINDI"
1111"BESS"
1112"IONA"
1113"HANNA"
1114"ARIEL"
1115"WINONA"
1116"VIDA"
1117"ROSITA"
1118"MARIANNA"
1119"WILLIAM"
1120"RACHEAL"
1121"GUILLERMINA"
1122"ELOISA"
1123"CELESTINE"
1124"CAREN"
1125"MALISSA"
1126"LONA"
1127"CHANTEL"
1128"SHELLIE"
1129"MARISELA"
1130"LEORA"
1131"AGATHA"
1132"SOLEDAD"
1133"MIGDALIA"
1134"IVETTE"
1135"CHRISTEN"
1136"ATHENA"
1137"JANEL"
1138"CHLOE"
1139"VEDA"
1140"PATTIE"
1141"TESSIE"
1142"TERA"
1143"MARILYNN"
1144"LUCRETIA"
1145"KARRIE"
1146"DINAH"
1147"DANIELA"
1148"ALECIA"
1149"ADELINA"
1150"VERNICE"
1151"SHIELA"
1152"PORTIA"
1153"MERRY"
1154"LASHAWN"
1155"DEVON"
1156"DARA"
1157"TAWANA"
1158"OMA"
1159"VERDA"
1160"CHRISTIN"
1161"ALENE"
1162"ZELLA"
1163"SANDI"
1164"RAFAELA"
1165"MAYA"
1166"KIRA"
1167"CANDIDA"
1168"ALVINA"
1169"SUZAN"
1170"SHAYLA"
1171"LYN"
1172"LETTIE"
1173"ALVA"
1174"SAMATHA"
1175"ORALIA"
1176"MATILDE"
1177"MADONNA"
1178"LARISSA"
1179"VESTA"
1180"RENITA"
1181"INDIA"
1182"DELOIS"
1183"SHANDA"
1184"PHILLIS"
1185"LORRI"
1186"ERLINDA"
1187"CRUZ"
1188"CATHRINE"
1189"BARB"
1190"ZOE"
1191"ISABELL"
1192"IONE"
1193"GISELA"
1194"CHARLIE"
1195"VALENCIA"
1196"ROXANNA"
1197"MAYME"
1198"KISHA"
1199"ELLIE"
1200"MELLISSA"
1201"DORRIS"
1202"DALIA"
1203"BELLA"
1204"ANNETTA"
1205"ZOILA"
1206"RETA"
1207"REINA"
1208"LAURETTA"
1209"KYLIE"
1210"CHRISTAL"
1211"PILAR"
1212"CHARLA"
1213"ELISSA"
1214"TIFFANI"
1215"TANA"
1216"PAULINA"
1217"LEOTA"
1218"BREANNA"
1219"JAYME"
1220"CARMEL"
1221"VERNELL"
1222"TOMASA"
1223"MANDI"
1224"DOMINGA"
1225"SANTA"
1226"MELODIE"
1227"LURA"
1228"ALEXA"
1229"TAMELA"
1230"RYAN"
1231"MIRNA"
1232"KERRIE"
1233"VENUS"
1234"NOEL"
1235"FELICITA"
1236"CRISTY"
1237"CARMELITA"
1238"BERNIECE"
1239"ANNEMARIE"
1240"TIARA"
1241"ROSEANNE"
1242"MISSY"
1243"CORI"
1244"ROXANA"
1245"PRICILLA"
1246"KRISTAL"
1247"JUNG"
1248"ELYSE"
1249"HAYDEE"
1250"ALETHA"
1251"BETTINA"
1252"MARGE"
1253"GILLIAN"
1254"FILOMENA"
1255"CHARLES"
1256"ZENAIDA"
1257"HARRIETTE"
1258"CARIDAD"
1259"VADA"
1260"UNA"
1261"ARETHA"
1262"PEARLINE"
1263"MARJORY"
1264"MARCELA"
1265"FLOR"
1266"EVETTE"
1267"ELOUISE"
1268"ALINA"
1269"TRINIDAD"
1270"DAVID"
1271"DAMARIS"
1272"CATHARINE"
1273"CARROLL"
1274"BELVA"
1275"NAKIA"
1276"MARLENA"
1277"LUANNE"
1278"LORINE"
1279"KARON"
1280"DORENE"
1281"DANITA"
1282"BRENNA"
1283"TATIANA"
1284"SAMMIE"
1285"LOUANN"
1286"LOREN"
1287"JULIANNA"
1288"ANDRIA"
1289"PHILOMENA"
1290"LUCILA"
1291"LEONORA"
1292"DOVIE"
1293"ROMONA"
1294"MIMI"
1295"JACQUELIN"
1296"GAYE"
1297"TONJA"
1298"MISTI"
1299"JOE"
1300"GENE"
1301"CHASTITY"
1302"STACIA"
1303"ROXANN"
1304"MICAELA"
1305"NIKITA"
1306"MEI"
1307"VELDA"
1308"MARLYS"
1309"JOHNNA"
1310"AURA"
1311"LAVERN"
1312"IVONNE"
1313"HAYLEY"
1314"NICKI"
1315"MAJORIE"
1316"HERLINDA"
1317"GEORGE"
1318"ALPHA"
1319"YADIRA"
1320"PERLA"
1321"GREGORIA"
1322"DANIEL"
1323"ANTONETTE"
1324"SHELLI"
1325"MOZELLE"
1326"MARIAH"
1327"JOELLE"
1328"CORDELIA"
1329"JOSETTE"
1330"CHIQUITA"
1331"TRISTA"
1332"LOUIS"
1333"LAQUITA"
1334"GEORGIANA"
1335"CANDI"
1336"SHANON"
1337"LONNIE"
1338"HILDEGARD"
1339"CECIL"
1340"VALENTINA"
1341"STEPHANY"
1342"MAGDA"
1343"KAROL"
1344"GERRY"
1345"GABRIELLA"
1346"TIANA"
1347"ROMA"
1348"RICHELLE"
1349"RAY"
1350"PRINCESS"
1351"OLETA"
1352"JACQUE"
1353"IDELLA"
1354"ALAINA"
1355"SUZANNA"
1356"JOVITA"
1357"BLAIR"
1358"TOSHA"
1359"RAVEN"
1360"NEREIDA"
1361"MARLYN"
1362"KYLA"
1363"JOSEPH"
1364"DELFINA"
1365"TENA"
1366"STEPHENIE"
1367"SABINA"
1368"NATHALIE"
1369"MARCELLE"
1370"GERTIE"
1371"DARLEEN"
1372"THEA"
1373"SHARONDA"
1374"SHANTEL"
1375"BELEN"
1376"VENESSA"
1377"ROSALINA"
1378"ONA"
1379"GENOVEVA"
1380"COREY"
1381"CLEMENTINE"
1382"ROSALBA"
1383"RENATE"
1384"RENATA"
1385"MI"
1386"IVORY"
1387"GEORGIANNA"
1388"FLOY"
1389"DORCAS"
1390"ARIANA"
1391"TYRA"
1392"THEDA"
1393"MARIAM"
1394"JULI"
1395"JESICA"
1396"DONNIE"
1397"VIKKI"
1398"VERLA"
1399"ROSELYN"
1400"MELVINA"
1401"JANNETTE"
1402"GINNY"
1403"DEBRAH"
1404"CORRIE"
1405"ASIA"
1406"VIOLETA"
1407"MYRTIS"
1408"LATRICIA"
1409"COLLETTE"
1410"CHARLEEN"
1411"ANISSA"
1412"VIVIANA"
1413"TWYLA"
1414"PRECIOUS"
1415"NEDRA"
1416"LATONIA"
1417"LAN"
1418"HELLEN"
1419"FABIOLA"
1420"ANNAMARIE"
1421"ADELL"
1422"SHARYN"
1423"CHANTAL"
1424"NIKI"
1425"MAUD"
1426"LIZETTE"
1427"LINDY"
1428"KIA"
1429"KESHA"
1430"JEANA"
1431"DANELLE"
1432"CHARLINE"
1433"CHANEL"
1434"CARROL"
1435"VALORIE"
1436"LIA"
1437"DORTHA"
1438"CRISTAL"
1439"SUNNY"
1440"LEONE"
1441"LEILANI"
1442"GERRI"
1443"DEBI"
1444"ANDRA"
1445"KESHIA"
1446"IMA"
1447"EULALIA"
1448"EASTER"
1449"DULCE"
1450"NATIVIDAD"
1451"LINNIE"
1452"KAMI"
1453"GEORGIE"
1454"CATINA"
1455"BROOK"
1456"ALDA"
1457"WINNIFRED"
1458"SHARLA"
1459"RUTHANN"
1460"MEAGHAN"
1461"MAGDALENE"
1462"LISSETTE"
1463"ADELAIDA"
1464"VENITA"
1465"TRENA"
1466"SHIRLENE"
1467"SHAMEKA"
1468"ELIZEBETH"
1469"DIAN"
1470"SHANTA"
1471"MICKEY"
1472"LATOSHA"
1473"CARLOTTA"
1474"WINDY"
1475"SOON"
1476"ROSINA"
1477"MARIANN"
1478"LEISA"
1479"JONNIE"
1480"DAWNA"
1481"CATHIE"
1482"BILLY"
1483"ASTRID"
1484"SIDNEY"
1485"LAUREEN"
1486"JANEEN"
1487"HOLLI"
1488"FAWN"
1489"VICKEY"
1490"TERESSA"
1491"SHANTE"
1492"RUBYE"
1493"MARCELINA"
1494"CHANDA"
1495"CARY"
1496"TERESE"
1497"SCARLETT"
1498"MARTY"
1499"MARNIE"
1500"LULU"
1501"LISETTE"
1502"JENIFFER"
1503"ELENOR"
1504"DORINDA"
1505"DONITA"
1506"CARMAN"
1507"BERNITA"
1508"ALTAGRACIA"
1509"ALETA"
1510"ADRIANNA"
1511"ZORAIDA"
1512"RONNIE"
1513"NICOLA"
1514"LYNDSEY"
1515"KENDALL"
1516"JANINA"
1517"CHRISSY"
1518"AMI"
1519"STARLA"
1520"PHYLIS"
1521"PHUONG"
1522"KYRA"
1523"CHARISSE"
1524"BLANCH"
1525"SANJUANITA"
1526"RONA"
1527"NANCI"
1528"MARILEE"
1529"MARANDA"
1530"CORY"
1531"BRIGETTE"
1532"SANJUANA"
1533"MARITA"
1534"KASSANDRA"
1535"JOYCELYN"
1536"IRA"
1537"FELIPA"
1538"CHELSIE"
1539"BONNY"
1540"MIREYA"
1541"LORENZA"
1542"KYONG"
1543"ILEANA"
1544"CANDELARIA"
1545"TONY"
1546"TOBY"
1547"SHERIE"
1548"OK"
1549"MARK"
1550"LUCIE"
1551"LEATRICE"
1552"LAKESHIA"
1553"GERDA"
1554"EDIE"
1555"BAMBI"
1556"MARYLIN"
1557"LAVON"
1558"HORTENSE"
1559"GARNET"
1560"EVIE"
1561"TRESSA"
1562"SHAYNA"
1563"LAVINA"
1564"KYUNG"
1565"JEANETTA"
1566"SHERRILL"
1567"SHARA"
1568"PHYLISS"
1569"MITTIE"
1570"ANABEL"
1571"ALESIA"
1572"THUY"
1573"TAWANDA"
1574"RICHARD"
1575"JOANIE"
1576"TIFFANIE"
1577"LASHANDA"
1578"KARISSA"
1579"ENRIQUETA"
1580"DARIA"
1581"DANIELLA"
1582"CORINNA"
1583"ALANNA"
1584"ABBEY"
1585"ROXANE"
1586"ROSEANNA"
1587"MAGNOLIA"
1588"LIDA"
1589"KYLE"
1590"JOELLEN"
1591"ERA"
1592"CORAL"
1593"CARLEEN"
1594"TRESA"
1595"PEGGIE"
1596"NOVELLA"
1597"NILA"
1598"MAYBELLE"
1599"JENELLE"
1600"CARINA"
1601"NOVA"
1602"MELINA"
1603"MARQUERITE"
1604"MARGARETTE"
1605"JOSEPHINA"
1606"EVONNE"
1607"DEVIN"
1608"CINTHIA"
1609"ALBINA"
1610"TOYA"
1611"TAWNYA"
1612"SHERITA"
1613"SANTOS"
1614"MYRIAM"
1615"LIZABETH"
1616"LISE"
1617"KEELY"
1618"JENNI"
1619"GISELLE"
1620"CHERYLE"
1621"ARDITH"
1622"ARDIS"
1623"ALESHA"
1624"ADRIANE"
1625"SHAINA"
1626"LINNEA"
1627"KAROLYN"
1628"HONG"
1629"FLORIDA"
1630"FELISHA"
1631"DORI"
1632"DARCI"
1633"ARTIE"
1634"ARMIDA"
1635"ZOLA"
1636"XIOMARA"
1637"VERGIE"
1638"SHAMIKA"
1639"NENA"
1640"NANNETTE"
1641"MAXIE"
1642"LOVIE"
1643"JEANE"
1644"JAIMIE"
1645"INGE"
1646"FARRAH"
1647"ELAINA"
1648"CAITLYN"
1649"STARR"
1650"FELICITAS"
1651"CHERLY"
1652"CARYL"
1653"YOLONDA"
1654"YASMIN"
1655"TEENA"
1656"PRUDENCE"
1657"PENNIE"
1658"NYDIA"
1659"MACKENZIE"
1660"ORPHA"
1661"MARVEL"
1662"LIZBETH"
1663"LAURETTE"
1664"JERRIE"
1665"HERMELINDA"
1666"CAROLEE"
1667"TIERRA"
1668"MIRIAN"
1669"META"
1670"MELONY"
1671"KORI"
1672"JENNETTE"
1673"JAMILA"
1674"ENA"
1675"ANH"
1676"YOSHIKO"
1677"SUSANNAH"
1678"SALINA"
1679"RHIANNON"
1680"JOLEEN"
1681"CRISTINE"
1682"ASHTON"
1683"ARACELY"
1684"TOMEKA"
1685"SHALONDA"
1686"MARTI"
1687"LACIE"
1688"KALA"
1689"JADA"
1690"ILSE"
1691"HAILEY"
1692"BRITTANI"
1693"ZONA"
1694"SYBLE"
1695"SHERRYL"
1696"RANDY"
1697"NIDIA"
1698"MARLO"
1699"KANDICE"
1700"KANDI"
1701"DEB"
1702"DEAN"
1703"AMERICA"
1704"ALYCIA"
1705"TOMMY"
1706"RONNA"
1707"NORENE"
1708"MERCY"
1709"JOSE"
1710"INGEBORG"
1711"GIOVANNA"
1712"GEMMA"
1713"CHRISTEL"
1714"AUDRY"
1715"ZORA"
1716"VITA"
1717"VAN"
1718"TRISH"
1719"STEPHAINE"
1720"SHIRLEE"
1721"SHANIKA"
1722"MELONIE"
1723"MAZIE"
1724"JAZMIN"
1725"INGA"
1726"HOA"
1727"HETTIE"
1728"GERALYN"
1729"FONDA"
1730"ESTRELLA"
1731"ADELLA"
1732"SU"
1733"SARITA"
1734"RINA"
1735"MILISSA"
1736"MARIBETH"
1737"GOLDA"
1738"EVON"
1739"ETHELYN"
1740"ENEDINA"
1741"CHERISE"
1742"CHANA"
1743"VELVA"
1744"TAWANNA"
1745"SADE"
1746"MIRTA"
1747"LI"
1748"KARIE"
1749"JACINTA"
1750"ELNA"
1751"DAVINA"
1752"CIERRA"
1753"ASHLIE"
1754"ALBERTHA"
1755"TANESHA"
1756"STEPHANI"
1757"NELLE"
1758"MINDI"
1759"LU"
1760"LORINDA"
1761"LARUE"
1762"FLORENE"
1763"DEMETRA"
1764"DEDRA"
1765"CIARA"
1766"CHANTELLE"
1767"ASHLY"
1768"SUZY"
1769"ROSALVA"
1770"NOELIA"
1771"LYDA"
1772"LEATHA"
1773"KRYSTYNA"
1774"KRISTAN"
1775"KARRI"
1776"DARLINE"
1777"DARCIE"
1778"CINDA"
1779"CHEYENNE"
1780"CHERRIE"
1781"AWILDA"
1782"ALMEDA"
1783"ROLANDA"
1784"LANETTE"
1785"JERILYN"
1786"GISELE"
1787"EVALYN"
1788"CYNDI"
1789"CLETA"
1790"CARIN"
1791"ZINA"
1792"ZENA"
1793"VELIA"
1794"TANIKA"
1795"PAUL"
1796"CHARISSA"
1797"THOMAS"
1798"TALIA"
1799"MARGARETE"
1800"LAVONDA"
1801"KAYLEE"
1802"KATHLENE"
1803"JONNA"
1804"IRENA"
1805"ILONA"
1806"IDALIA"
1807"CANDIS"
1808"CANDANCE"
1809"BRANDEE"
1810"ANITRA"
1811"ALIDA"
1812"SIGRID"
1813"NICOLETTE"
1814"MARYJO"
1815"LINETTE"
1816"HEDWIG"
1817"CHRISTIANA"
1818"CASSIDY"
1819"ALEXIA"
1820"TRESSIE"
1821"MODESTA"
1822"LUPITA"
1823"LITA"
1824"GLADIS"
1825"EVELIA"
1826"DAVIDA"
1827"CHERRI"
1828"CECILY"
1829"ASHELY"
1830"ANNABEL"
1831"AGUSTINA"
1832"WANITA"
1833"SHIRLY"
1834"ROSAURA"
1835"HULDA"
1836"EUN"
1837"BAILEY"
1838"YETTA"
1839"VERONA"
1840"THOMASINA"
1841"SIBYL"
1842"SHANNAN"
1843"MECHELLE"
1844"LUE"
1845"LEANDRA"
1846"LANI"
1847"KYLEE"
1848"KANDY"
1849"JOLYNN"
1850"FERNE"
1851"EBONI"
1852"CORENE"
1853"ALYSIA"
1854"ZULA"
1855"NADA"
1856"MOIRA"
1857"LYNDSAY"
1858"LORRETTA"
1859"JUAN"
1860"JAMMIE"
1861"HORTENSIA"
1862"GAYNELL"
1863"CAMERON"
1864"ADRIA"
1865"VINA"
1866"VICENTA"
1867"TANGELA"
1868"STEPHINE"
1869"NORINE"
1870"NELLA"
1871"LIANA"
1872"LESLEE"
1873"KIMBERELY"
1874"ILIANA"
1875"GLORY"
1876"FELICA"
1877"EMOGENE"
1878"ELFRIEDE"
1879"EDEN"
1880"EARTHA"
1881"CARMA"
1882"BEA"
1883"OCIE"
1884"MARRY"
1885"LENNIE"
1886"KIARA"
1887"JACALYN"
1888"CARLOTA"
1889"ARIELLE"
1890"YU"
1891"STAR"
1892"OTILIA"
1893"KIRSTIN"
1894"KACEY"
1895"JOHNETTA"
1896"JOEY"
1897"JOETTA"
1898"JERALDINE"
1899"JAUNITA"
1900"ELANA"
1901"DORTHEA"
1902"CAMI"
1903"AMADA"
1904"ADELIA"
1905"VERNITA"
1906"TAMAR"
1907"SIOBHAN"
1908"RENEA"
1909"RASHIDA"
1910"OUIDA"
1911"ODELL"
1912"NILSA"
1913"MERYL"
1914"KRISTYN"
1915"JULIETA"
1916"DANICA"
1917"BREANNE"
1918"AUREA"
1919"ANGLEA"
1920"SHERRON"
1921"ODETTE"
1922"MALIA"
1923"LORELEI"
1924"LIN"
1925"LEESA"
1926"KENNA"
1927"KATHLYN"
1928"FIONA"
1929"CHARLETTE"
1930"SUZIE"
1931"SHANTELL"
1932"SABRA"
1933"RACQUEL"
1934"MYONG"
1935"MIRA"
1936"MARTINE"
1937"LUCIENNE"
1938"LAVADA"
1939"JULIANN"
1940"JOHNIE"
1941"ELVERA"
1942"DELPHIA"
1943"CLAIR"
1944"CHRISTIANE"
1945"CHAROLETTE"
1946"CARRI"
1947"AUGUSTINE"
1948"ASHA"
1949"ANGELLA"
1950"PAOLA"
1951"NINFA"
1952"LEDA"
1953"LAI"
1954"EDA"
1955"SUNSHINE"
1956"STEFANI"
1957"SHANELL"
1958"PALMA"
1959"MACHELLE"
1960"LISSA"
1961"KECIA"
1962"KATHRYNE"
1963"KARLENE"
1964"JULISSA"
1965"JETTIE"
1966"JENNIFFER"
1967"HUI"
1968"CORRINA"
1969"CHRISTOPHER"
1970"CAROLANN"
1971"ALENA"
1972"TESS"
1973"ROSARIA"
1974"MYRTICE"
1975"MARYLEE"
1976"LIANE"
1977"KENYATTA"
1978"JUDIE"
1979"JANEY"
1980"IN"
1981"ELMIRA"
1982"ELDORA"
1983"DENNA"
1984"CRISTI"
1985"CATHI"
1986"ZAIDA"
1987"VONNIE"
1988"VIVA"
1989"VERNIE"
1990"ROSALINE"
1991"MARIELA"
1992"LUCIANA"
1993"LESLI"
1994"KARAN"
1995"FELICE"
1996"DENEEN"
1997"ADINA"
1998"WYNONA"
1999"TARSHA"
2000"SHERON"
2001"SHASTA"
2002"SHANITA"
2003"SHANI"
2004"SHANDRA"
2005"RANDA"
2006"PINKIE"
2007"PARIS"
2008"NELIDA"
2009"MARILOU"
2010"LYLA"
2011"LAURENE"
2012"LACI"
2013"JOI"
2014"JANENE"
2015"DOROTHA"
2016"DANIELE"
2017"DANI"
2018"CAROLYNN"
2019"CARLYN"
2020"BERENICE"
2021"AYESHA"
2022"ANNELIESE"
2023"ALETHEA"
2024"THERSA"
2025"TAMIKO"
2026"RUFINA"
2027"OLIVA"
2028"MOZELL"
2029"MARYLYN"
2030"MADISON"
2031"KRISTIAN"
2032"KATHYRN"
2033"KASANDRA"
2034"KANDACE"
2035"JANAE"
2036"GABRIEL"
2037"DOMENICA"
2038"DEBBRA"
2039"DANNIELLE"
2040"CHUN"
2041"BUFFY"
2042"BARBIE"
2043"ARCELIA"
2044"AJA"
2045"ZENOBIA"
2046"SHAREN"
2047"SHAREE"
2048"PATRICK"
2049"PAGE"
2050"MY"
2051"LAVINIA"
2052"KUM"
2053"KACIE"
2054"JACKELINE"
2055"HUONG"
2056"FELISA"
2057"EMELIA"
2058"ELEANORA"
2059"CYTHIA"
2060"CRISTIN"
2061"CLYDE"
2062"CLARIBEL"
2063"CARON"
2064"ANASTACIA"
2065"ZULMA"
2066"ZANDRA"
2067"YOKO"
2068"TENISHA"
2069"SUSANN"
2070"SHERILYN"
2071"SHAY"
2072"SHAWANDA"
2073"SABINE"
2074"ROMANA"
2075"MATHILDA"
2076"LINSEY"
2077"KEIKO"
2078"JOANA"
2079"ISELA"
2080"GRETTA"
2081"GEORGETTA"
2082"EUGENIE"
2083"DUSTY"
2084"DESIRAE"
2085"DELORA"
2086"CORAZON"
2087"ANTONINA"
2088"ANIKA"
2089"WILLENE"
2090"TRACEE"
2091"TAMATHA"
2092"REGAN"
2093"NICHELLE"
2094"MICKIE"
2095"MAEGAN"
2096"LUANA"
2097"LANITA"
2098"KELSIE"
2099"EDELMIRA"
2100"BREE"
2101"AFTON"
2102"TEODORA"
2103"TAMIE"
2104"SHENA"
2105"MEG"
2106"LINH"
2107"KELI"
2108"KACI"
2109"DANYELLE"
2110"BRITT"
2111"ARLETTE"
2112"ALBERTINE"
2113"ADELLE"
2114"TIFFINY"
2115"STORMY"
2116"SIMONA"
2117"NUMBERS"
2118"NICOLASA"
2119"NICHOL"
2120"NIA"
2121"NAKISHA"
2122"MEE"
2123"MAIRA"
2124"LOREEN"
2125"KIZZY"
2126"JOHNNY"
2127"JAY"
2128"FALLON"
2129"CHRISTENE"
2130"BOBBYE"
2131"ANTHONY"
2132"YING"
2133"VINCENZA"
2134"TANJA"
2135"RUBIE"
2136"RONI"
2137"QUEENIE"
2138"MARGARETT"
2139"KIMBERLI"
2140"IRMGARD"
2141"IDELL"
2142"HILMA"
2143"EVELINA"
2144"ESTA"
2145"EMILEE"
2146"DENNISE"
2147"DANIA"
2148"CARL"
2149"CARIE"
2150"ANTONIO"
2151"WAI"
2152"SANG"
2153"RISA"
2154"RIKKI"
2155"PARTICIA"
2156"MUI"
2157"MASAKO"
2158"MARIO"
2159"LUVENIA"
2160"LOREE"
2161"LONI"
2162"LIEN"
2163"KEVIN"
2164"GIGI"
2165"FLORENCIA"
2166"DORIAN"
2167"DENITA"
2168"DALLAS"
2169"CHI"
2170"BILLYE"
2171"ALEXANDER"
2172"TOMIKA"
2173"SHARITA"
2174"RANA"
2175"NIKOLE"
2176"NEOMA"
2177"MARGARITE"
2178"MADALYN"
2179"LUCINA"
2180"LAILA"
2181"KALI"
2182"JENETTE"
2183"GABRIELE"
2184"EVELYNE"
2185"ELENORA"
2186"CLEMENTINA"
2187"ALEJANDRINA"
2188"ZULEMA"
2189"VIOLETTE"
2190"VANNESSA"
2191"THRESA"
2192"RETTA"
2193"PIA"
2194"PATIENCE"
2195"NOELLA"
2196"NICKIE"
2197"JONELL"
2198"DELTA"
2199"CHUNG"
2200"CHAYA"
2201"CAMELIA"
2202"BETHEL"
2203"ANYA"
2204"ANDREW"
2205"THANH"
2206"SUZANN"
2207"SPRING"
2208"SHU"
2209"MILA"
2210"LILLA"
2211"LAVERNA"
2212"KEESHA"
2213"KATTIE"
2214"GIA"
2215"GEORGENE"
2216"EVELINE"
2217"ESTELL"
2218"ELIZBETH"
2219"VIVIENNE"
2220"VALLIE"
2221"TRUDIE"
2222"STEPHANE"
2223"MICHEL"
2224"MAGALY"
2225"MADIE"
2226"KENYETTA"
2227"KARREN"
2228"JANETTA"
2229"HERMINE"
2230"HARMONY"
2231"DRUCILLA"
2232"DEBBI"
2233"CELESTINA"
2234"CANDIE"
2235"BRITNI"
2236"BECKIE"
2237"AMINA"
2238"ZITA"
2239"YUN"
2240"YOLANDE"
2241"VIVIEN"
2242"VERNETTA"
2243"TRUDI"
2244"SOMMER"
2245"PEARLE"
2246"PATRINA"
2247"OSSIE"
2248"NICOLLE"
2249"LOYCE"
2250"LETTY"
2251"LARISA"
2252"KATHARINA"
2253"JOSELYN"
2254"JONELLE"
2255"JENELL"
2256"IESHA"
2257"HEIDE"
2258"FLORINDA"
2259"FLORENTINA"
2260"FLO"
2261"ELODIA"
2262"DORINE"
2263"BRUNILDA"
2264"BRIGID"
2265"ASHLI"
2266"ARDELLA"
2267"TWANA"
2268"THU"
2269"TARAH"
2270"SUNG"
2271"SHEA"
2272"SHAVON"
2273"SHANE"
2274"SERINA"
2275"RAYNA"
2276"RAMONITA"
2277"NGA"
2278"MARGURITE"
2279"LUCRECIA"
2280"KOURTNEY"
2281"KATI"
2282"JESUS"
2283"JESENIA"
2284"DIAMOND"
2285"CRISTA"
2286"AYANA"
2287"ALICA"
2288"ALIA"
2289"VINNIE"
2290"SUELLEN"
2291"ROMELIA"
2292"RACHELL"
2293"PIPER"
2294"OLYMPIA"
2295"MICHIKO"
2296"KATHALEEN"
2297"JOLIE"
2298"JESSI"
2299"JANESSA"
2300"HANA"
2301"HA"
2302"ELEASE"
2303"CARLETTA"
2304"BRITANY"
2305"SHONA"
2306"SALOME"
2307"ROSAMOND"
2308"REGENA"
2309"RAINA"
2310"NGOC"
2311"NELIA"
2312"LOUVENIA"
2313"LESIA"
2314"LATRINA"
2315"LATICIA"
2316"LARHONDA"
2317"JINA"
2318"JACKI"
2319"HOLLIS"
2320"HOLLEY"
2321"EMMY"
2322"DEEANN"
2323"CORETTA"
2324"ARNETTA"
2325"VELVET"
2326"THALIA"
2327"SHANICE"
2328"NETA"
2329"MIKKI"
2330"MICKI"
2331"LONNA"
2332"LEANA"
2333"LASHUNDA"
2334"KILEY"
2335"JOYE"
2336"JACQULYN"
2337"IGNACIA"
2338"HYUN"
2339"HIROKO"
2340"HENRY"
2341"HENRIETTE"
2342"ELAYNE"
2343"DELINDA"
2344"DARNELL"
2345"DAHLIA"
2346"COREEN"
2347"CONSUELA"
2348"CONCHITA"
2349"CELINE"
2350"BABETTE"
2351"AYANNA"
2352"ANETTE"
2353"ALBERTINA"
2354"SKYE"
2355"SHAWNEE"
2356"SHANEKA"
2357"QUIANA"
2358"PAMELIA"
2359"MIN"
2360"MERRI"
2361"MERLENE"
2362"MARGIT"
2363"KIESHA"
2364"KIERA"
2365"KAYLENE"
2366"JODEE"
2367"JENISE"
2368"ERLENE"
2369"EMMIE"
2370"ELSE"
2371"DARYL"
2372"DALILA"
2373"DAISEY"
2374"CODY"
2375"CASIE"
2376"BELIA"
2377"BABARA"
2378"VERSIE"
2379"VANESA"
2380"SHELBA"
2381"SHAWNDA"
2382"SAM"
2383"NORMAN"
2384"NIKIA"
2385"NAOMA"
2386"MARNA"
2387"MARGERET"
2388"MADALINE"
2389"LAWANA"
2390"KINDRA"
2391"JUTTA"
2392"JAZMINE"
2393"JANETT"
2394"HANNELORE"
2395"GLENDORA"
2396"GERTRUD"
2397"GARNETT"
2398"FREEDA"
2399"FREDERICA"
2400"FLORANCE"
2401"FLAVIA"
2402"DENNIS"
2403"CARLINE"
2404"BEVERLEE"
2405"ANJANETTE"
2406"VALDA"
2407"TRINITY"
2408"TAMALA"
2409"STEVIE"
2410"SHONNA"
2411"SHA"
2412"SARINA"
2413"ONEIDA"
2414"MICAH"
2415"MERILYN"
2416"MARLEEN"
2417"LURLINE"
2418"LENNA"
2419"KATHERIN"
2420"JIN"
2421"JENI"
2422"HAE"
2423"GRACIA"
2424"GLADY"
2425"FARAH"
2426"ERIC"
2427"ENOLA"
2428"EMA"
2429"DOMINQUE"
2430"DEVONA"
2431"DELANA"
2432"CECILA"
2433"CAPRICE"
2434"ALYSHA"
2435"ALI"
2436"ALETHIA"
2437"VENA"
2438"THERESIA"
2439"TAWNY"
2440"SONG"
2441"SHAKIRA"
2442"SAMARA"
2443"SACHIKO"
2444"RACHELE"
2445"PAMELLA"
2446"NICKY"
2447"MARNI"
2448"MARIEL"
2449"MAREN"
2450"MALISA"
2451"LIGIA"
2452"LERA"
2453"LATORIA"
2454"LARAE"
2455"KIMBER"
2456"KATHERN"
2457"KAREY"
2458"JENNEFER"
2459"JANETH"
2460"HALINA"
2461"FREDIA"
2462"DELISA"
2463"DEBROAH"
2464"CIERA"
2465"CHIN"
2466"ANGELIKA"
2467"ANDREE"
2468"ALTHA"
2469"YEN"
2470"VIVAN"
2471"TERRESA"
2472"TANNA"
2473"SUK"
2474"SUDIE"
2475"SOO"
2476"SIGNE"
2477"SALENA"
2478"RONNI"
2479"REBBECCA"
2480"MYRTIE"
2481"MCKENZIE"
2482"MALIKA"
2483"MAIDA"
2484"LOAN"
2485"LEONARDA"
2486"KAYLEIGH"
2487"FRANCE"
2488"ETHYL"
2489"ELLYN"
2490"DAYLE"
2491"CAMMIE"
2492"BRITTNI"
2493"BIRGIT"
2494"AVELINA"
2495"ASUNCION"
2496"ARIANNA"
2497"AKIKO"
2498"VENICE"
2499"TYESHA"
2500"TONIE"
2501"TIESHA"
2502"TAKISHA"
2503"STEFFANIE"
2504"SINDY"
2505"SANTANA"
2506"MEGHANN"
2507"MANDA"
2508"MACIE"
2509"LADY"
2510"KELLYE"
2511"KELLEE"
2512"JOSLYN"
2513"JASON"
2514"INGER"
2515"INDIRA"
2516"GLINDA"
2517"GLENNIS"
2518"FERNANDA"
2519"FAUSTINA"
2520"ENEIDA"
2521"ELICIA"
2522"DOT"
2523"DIGNA"
2524"DELL"
2525"ARLETTA"
2526"ANDRE"
2527"WILLIA"
2528"TAMMARA"
2529"TABETHA"
2530"SHERRELL"
2531"SARI"
2532"REFUGIO"
2533"REBBECA"
2534"PAULETTA"
2535"NIEVES"
2536"NATOSHA"
2537"NAKITA"
2538"MAMMIE"
2539"KENISHA"
2540"KAZUKO"
2541"KASSIE"
2542"GARY"
2543"EARLEAN"
2544"DAPHINE"
2545"CORLISS"
2546"CLOTILDE"
2547"CAROLYNE"
2548"BERNETTA"
2549"AUGUSTINA"
2550"AUDREA"
2551"ANNIS"
2552"ANNABELL"
2553"YAN"
2554"TENNILLE"
2555"TAMICA"
2556"SELENE"
2557"SEAN"
2558"ROSANA"
2559"REGENIA"
2560"QIANA"
2561"MARKITA"
2562"MACY"
2563"LEEANNE"
2564"LAURINE"
2565"KYM"
2566"JESSENIA"
2567"JANITA"
2568"GEORGINE"
2569"GENIE"
2570"EMIKO"
2571"ELVIE"
2572"DEANDRA"
2573"DAGMAR"
2574"CORIE"
2575"COLLEN"
2576"CHERISH"
2577"ROMAINE"
2578"PORSHA"
2579"PEARLENE"
2580"MICHELINE"
2581"MERNA"
2582"MARGORIE"
2583"MARGARETTA"
2584"LORE"
2585"KENNETH"
2586"JENINE"
2587"HERMINA"
2588"FREDERICKA"
2589"ELKE"
2590"DRUSILLA"
2591"DORATHY"
2592"DIONE"
2593"DESIRE"
2594"CELENA"
2595"BRIGIDA"
2596"ANGELES"
2597"ALLEGRA"
2598"THEO"
2599"TAMEKIA"
2600"SYNTHIA"
2601"STEPHEN"
2602"SOOK"
2603"SLYVIA"
2604"ROSANN"
2605"REATHA"
2606"RAYE"
2607"MARQUETTA"
2608"MARGART"
2609"LING"
2610"LAYLA"
2611"KYMBERLY"
2612"KIANA"
2613"KAYLEEN"
2614"KATLYN"
2615"KARMEN"
2616"JOELLA"
2617"IRINA"
2618"EMELDA"
2619"ELENI"
2620"DETRA"
2621"CLEMMIE"
2622"CHERYLL"
2623"CHANTELL"
2624"CATHEY"
2625"ARNITA"
2626"ARLA"
2627"ANGLE"
2628"ANGELIC"
2629"ALYSE"
2630"ZOFIA"
2631"THOMASINE"
2632"TENNIE"
2633"SON"
2634"SHERLY"
2635"SHERLEY"
2636"SHARYL"
2637"REMEDIOS"
2638"PETRINA"
2639"NICKOLE"
2640"MYUNG"
2641"MYRLE"
2642"MOZELLA"
2643"LOUANNE"
2644"LISHA"
2645"LATIA"
2646"LANE"
2647"KRYSTA"
2648"JULIENNE"
2649"JOEL"
2650"JEANENE"
2651"JACQUALINE"
2652"ISAURA"
2653"GWENDA"
2654"EARLEEN"
2655"DONALD"
2656"CLEOPATRA"
2657"CARLIE"
2658"AUDIE"
2659"ANTONIETTA"
2660"ALISE"
2661"ALEX"
2662"VERDELL"
2663"VAL"
2664"TYLER"
2665"TOMOKO"
2666"THAO"
2667"TALISHA"
2668"STEVEN"
2669"SO"
2670"SHEMIKA"
2671"SHAUN"
2672"SCARLET"
2673"SAVANNA"
2674"SANTINA"
2675"ROSIA"
2676"RAEANN"
2677"ODILIA"
2678"NANA"
2679"MINNA"
2680"MAGAN"
2681"LYNELLE"
2682"LE"
2683"KARMA"
2684"JOEANN"
2685"IVANA"
2686"INELL"
2687"ILANA"
2688"HYE"
2689"HONEY"
2690"HEE"
2691"GUDRUN"
2692"FRANK"
2693"DREAMA"
2694"CRISSY"
2695"CHANTE"
2696"CARMELINA"
2697"ARVILLA"
2698"ARTHUR"
2699"ANNAMAE"
2700"ALVERA"
2701"ALEIDA"
2702"AARON"
2703"YEE"
2704"YANIRA"
2705"VANDA"
2706"TIANNA"
2707"TAM"
2708"STEFANIA"
2709"SHIRA"
2710"PERRY"
2711"NICOL"
2712"NANCIE"
2713"MONSERRATE"
2714"MINH"
2715"MELYNDA"
2716"MELANY"
2717"MATTHEW"
2718"LOVELLA"
2719"LAURE"
2720"KIRBY"
2721"KACY"
2722"JACQUELYNN"
2723"HYON"
2724"GERTHA"
2725"FRANCISCO"
2726"ELIANA"
2727"CHRISTENA"
2728"CHRISTEEN"
2729"CHARISE"
2730"CATERINA"
2731"CARLEY"
2732"CANDYCE"
2733"ARLENA"
2734"AMMIE"
2735"YANG"
2736"WILLETTE"
2737"VANITA"
2738"TUYET"
2739"TINY"
2740"SYREETA"
2741"SILVA"
2742"SCOTT"
2743"RONALD"
2744"PENNEY"
2745"NYLA"
2746"MICHAL"
2747"MAURICE"
2748"MARYAM"
2749"MARYA"
2750"MAGEN"
2751"LUDIE"
2752"LOMA"
2753"LIVIA"
2754"LANELL"
2755"KIMBERLIE"
2756"JULEE"
2757"DONETTA"
2758"DIEDRA"
2759"DENISHA"
2760"DEANE"
2761"DAWNE"
2762"CLARINE"
2763"CHERRYL"
2764"BRONWYN"
2765"BRANDON"
2766"ALLA"
2767"VALERY"
2768"TONDA"
2769"SUEANN"
2770"SORAYA"
2771"SHOSHANA"
2772"SHELA"
2773"SHARLEEN"
2774"SHANELLE"
2775"NERISSA"
2776"MICHEAL"
2777"MERIDITH"
2778"MELLIE"
2779"MAYE"
2780"MAPLE"
2781"MAGARET"
2782"LUIS"
2783"LILI"
2784"LEONILA"
2785"LEONIE"
2786"LEEANNA"
2787"LAVONIA"
2788"LAVERA"
2789"KRISTEL"
2790"KATHEY"
2791"KATHE"
2792"JUSTIN"
2793"JULIAN"
2794"JIMMY"
2795"JANN"
2796"ILDA"
2797"HILDRED"
2798"HILDEGARDE"
2799"GENIA"
2800"FUMIKO"
2801"EVELIN"
2802"ERMELINDA"
2803"ELLY"
2804"DUNG"
2805"DOLORIS"
2806"DIONNA"
2807"DANAE"
2808"BERNEICE"
2809"ANNICE"
2810"ALIX"
2811"VERENA"
2812"VERDIE"
2813"TRISTAN"
2814"SHAWNNA"
2815"SHAWANA"
2816"SHAUNNA"
2817"ROZELLA"
2818"RANDEE"
2819"RANAE"
2820"MILAGRO"
2821"LYNELL"
2822"LUISE"
2823"LOUIE"
2824"LOIDA"
2825"LISBETH"
2826"KARLEEN"
2827"JUNITA"
2828"JONA"
2829"ISIS"
2830"HYACINTH"
2831"HEDY"
2832"GWENN"
2833"ETHELENE"
2834"ERLINE"
2835"EDWARD"
2836"DONYA"
2837"DOMONIQUE"
2838"DELICIA"
2839"DANNETTE"
2840"CICELY"
2841"BRANDA"
2842"BLYTHE"
2843"BETHANN"
2844"ASHLYN"
2845"ANNALEE"
2846"ALLINE"
2847"YUKO"
2848"VELLA"
2849"TRANG"
2850"TOWANDA"
2851"TESHA"
2852"SHERLYN"
2853"NARCISA"
2854"MIGUELINA"
2855"MERI"
2856"MAYBELL"
2857"MARLANA"
2858"MARGUERITA"
2859"MADLYN"
2860"LUNA"
2861"LORY"
2862"LORIANN"
2863"LIBERTY"
2864"LEONORE"
2865"LEIGHANN"
2866"LAURICE"
2867"LATESHA"
2868"LARONDA"
2869"KATRICE"
2870"KASIE"
2871"KARL"
2872"KALEY"
2873"JADWIGA"
2874"GLENNIE"
2875"GEARLDINE"
2876"FRANCINA"
2877"EPIFANIA"
2878"DYAN"
2879"DORIE"
2880"DIEDRE"
2881"DENESE"
2882"DEMETRICE"
2883"DELENA"
2884"DARBY"
2885"CRISTIE"
2886"CLEORA"
2887"CATARINA"
2888"CARISA"
2889"BERNIE"
2890"BARBERA"
2891"ALMETA"
2892"TRULA"
2893"TEREASA"
2894"SOLANGE"
2895"SHEILAH"
2896"SHAVONNE"
2897"SANORA"
2898"ROCHELL"
2899"MATHILDE"
2900"MARGARETA"
2901"MAIA"
2902"LYNSEY"
2903"LAWANNA"
2904"LAUNA"
2905"KENA"
2906"KEENA"
2907"KATIA"
2908"JAMEY"
2909"GLYNDA"
2910"GAYLENE"
2911"ELVINA"
2912"ELANOR"
2913"DANUTA"
2914"DANIKA"
2915"CRISTEN"
2916"CORDIE"
2917"COLETTA"
2918"CLARITA"
2919"CARMON"
2920"BRYNN"
2921"AZUCENA"
2922"AUNDREA"
2923"ANGELE"
2924"YI"
2925"WALTER"
2926"VERLIE"
2927"VERLENE"
2928"TAMESHA"
2929"SILVANA"
2930"SEBRINA"
2931"SAMIRA"
2932"REDA"
2933"RAYLENE"
2934"PENNI"
2935"PANDORA"
2936"NORAH"
2937"NOMA"
2938"MIREILLE"
2939"MELISSIA"
2940"MARYALICE"
2941"LARAINE"
2942"KIMBERY"
2943"KARYL"
2944"KARINE"
2945"KAM"
2946"JOLANDA"
2947"JOHANA"
2948"JESUSA"
2949"JALEESA"
2950"JAE"
2951"JACQUELYNE"
2952"IRISH"
2953"ILUMINADA"
2954"HILARIA"
2955"HANH"
2956"GENNIE"
2957"FRANCIE"
2958"FLORETTA"
2959"EXIE"
2960"EDDA"
2961"DREMA"
2962"DELPHA"
2963"BEV"
2964"BARBAR"
2965"ASSUNTA"
2966"ARDELL"
2967"ANNALISA"
2968"ALISIA"
2969"YUKIKO"
2970"YOLANDO"
2971"WONDA"
2972"WEI"
2973"WALTRAUD"
2974"VETA"
2975"TEQUILA"
2976"TEMEKA"
2977"TAMEIKA"
2978"SHIRLEEN"
2979"SHENITA"
2980"PIEDAD"
2981"OZELLA"
2982"MIRTHA"
2983"MARILU"
2984"KIMIKO"
2985"JULIANE"
2986"JENICE"
2987"JEN"
2988"JANAY"
2989"JACQUILINE"
2990"HILDE"
2991"FE"
2992"FAE"
2993"EVAN"
2994"EUGENE"
2995"ELOIS"
2996"ECHO"
2997"DEVORAH"
2998"CHAU"
2999"BRINDA"
3000"BETSEY"
3001"ARMINDA"
3002"ARACELIS"
3003"APRYL"
3004"ANNETT"
3005"ALISHIA"
3006"VEOLA"
3007"USHA"
3008"TOSHIKO"
3009"THEOLA"
3010"TASHIA"
3011"TALITHA"
3012"SHERY"
3013"RUDY"
3014"RENETTA"
3015"REIKO"
3016"RASHEEDA"
3017"OMEGA"
3018"OBDULIA"
3019"MIKA"
3020"MELAINE"
3021"MEGGAN"
3022"MARTIN"
3023"MARLEN"
3024"MARGET"
3025"MARCELINE"
3026"MANA"
3027"MAGDALEN"
3028"LIBRADA"
3029"LEZLIE"
3030"LEXIE"
3031"LATASHIA"
3032"LASANDRA"
3033"KELLE"
3034"ISIDRA"
3035"ISA"
3036"INOCENCIA"
3037"GWYN"
3038"FRANCOISE"
3039"ERMINIA"
3040"ERINN"
3041"DIMPLE"
3042"DEVORA"
3043"CRISELDA"
3044"ARMANDA"
3045"ARIE"
3046"ARIANE"
3047"ANGELO"
3048"ANGELENA"
3049"ALLEN"
3050"ALIZA"
3051"ADRIENE"
3052"ADALINE"
3053"XOCHITL"
3054"TWANNA"
3055"TRAN"
3056"TOMIKO"
3057"TAMISHA"
3058"TAISHA"
3059"SUSY"
3060"SIU"
3061"RUTHA"
3062"ROXY"
3063"RHONA"
3064"RAYMOND"
3065"OTHA"
3066"NORIKO"
3067"NATASHIA"
3068"MERRIE"
3069"MELVIN"
3070"MARINDA"
3071"MARIKO"
3072"MARGERT"
3073"LORIS"
3074"LIZZETTE"
3075"LEISHA"
3076"KAILA"
3077"KA"
3078"JOANNIE"
3079"JERRICA"
3080"JENE"
3081"JANNET"
3082"JANEE"
3083"JACINDA"
3084"HERTA"
3085"ELENORE"
3086"DORETTA"
3087"DELAINE"
3088"DANIELL"
3089"CLAUDIE"
3090"CHINA"
3091"BRITTA"
3092"APOLONIA"
3093"AMBERLY"
3094"ALEASE"
3095"YURI"
3096"YUK"
3097"WEN"
3098"WANETA"
3099"UTE"
3100"TOMI"
3101"SHARRI"
3102"SANDIE"
3103"ROSELLE"
3104"REYNALDA"
3105"RAGUEL"
3106"PHYLICIA"
3107"PATRIA"
3108"OLIMPIA"
3109"ODELIA"
3110"MITZIE"
3111"MITCHELL"
3112"MISS"
3113"MINDA"
3114"MIGNON"
3115"MICA"
3116"MENDY"
3117"MARIVEL"
3118"MAILE"
3119"LYNETTA"
3120"LAVETTE"
3121"LAURYN"
3122"LATRISHA"
3123"LAKIESHA"
3124"KIERSTEN"
3125"KARY"
3126"JOSPHINE"
3127"JOLYN"
3128"JETTA"
3129"JANISE"
3130"JACQUIE"
3131"IVELISSE"
3132"GLYNIS"
3133"GIANNA"
3134"GAYNELLE"
3135"EMERALD"
3136"DEMETRIUS"
3137"DANYELL"
3138"DANILLE"
3139"DACIA"
3140"CORALEE"
3141"CHER"
3142"CEOLA"
3143"BRETT"
3144"BELL"
3145"ARIANNE"
3146"ALESHIA"
3147"YUNG"
3148"WILLIEMAE"
3149"TROY"
3150"TRINH"
3151"THORA"
3152"TAI"
3153"SVETLANA"
3154"SHERIKA"
3155"SHEMEKA"
3156"SHAUNDA"
3157"ROSELINE"
3158"RICKI"
3159"MELDA"
3160"MALLIE"
3161"LAVONNA"
3162"LATINA"
3163"LARRY"
3164"LAQUANDA"
3165"LALA"
3166"LACHELLE"
3167"KLARA"
3168"KANDIS"
3169"JOHNA"
3170"JEANMARIE"
3171"JAYE"
3172"HANG"
3173"GRAYCE"
3174"GERTUDE"
3175"EMERITA"
3176"EBONIE"
3177"CLORINDA"
3178"CHING"
3179"CHERY"
3180"CAROLA"
3181"BREANN"
3182"BLOSSOM"
3183"BERNARDINE"
3184"BECKI"
3185"ARLETHA"
3186"ARGELIA"
3187"ARA"
3188"ALITA"
3189"YULANDA"
3190"YON"
3191"YESSENIA"
3192"TOBI"
3193"TASIA"
3194"SYLVIE"
3195"SHIRL"
3196"SHIRELY"
3197"SHERIDAN"
3198"SHELLA"
3199"SHANTELLE"
3200"SACHA"
3201"ROYCE"
3202"REBECKA"
3203"REAGAN"
3204"PROVIDENCIA"
3205"PAULENE"
3206"MISHA"
3207"MIKI"
3208"MARLINE"
3209"MARICA"
3210"LORITA"
3211"LATOYIA"
3212"LASONYA"
3213"KERSTIN"
3214"KENDA"
3215"KEITHA"
3216"KATHRIN"
3217"JAYMIE"
3218"JACK"
3219"GRICELDA"
3220"GINETTE"
3221"ERYN"
3222"ELINA"
3223"ELFRIEDA"
3224"DANYEL"
3225"CHEREE"
3226"CHANELLE"
3227"BARRIE"
3228"AVERY"
3229"AURORE"
3230"ANNAMARIA"
3231"ALLEEN"
3232"AILENE"
3233"AIDE"
3234"YASMINE"
3235"VASHTI"
3236"VALENTINE"
3237"TREASA"
3238"TORY"
3239"TIFFANEY"
3240"SHERYLL"
3241"SHARIE"
3242"SHANAE"
3243"SAU"
3244"RAISA"
3245"PA"
3246"NEDA"
3247"MITSUKO"
3248"MIRELLA"
3249"MILDA"
3250"MARYANNA"
3251"MARAGRET"
3252"MABELLE"
3253"LUETTA"
3254"LORINA"
3255"LETISHA"
3256"LATARSHA"
3257"LANELLE"
3258"LAJUANA"
3259"KRISSY"
3260"KARLY"
3261"KARENA"
3262"JON"
3263"JESSIKA"
3264"JERICA"
3265"JEANELLE"
3266"JANUARY"
3267"JALISA"
3268"JACELYN"
3269"IZOLA"
3270"IVEY"
3271"GREGORY"
3272"EUNA"
3273"ETHA"
3274"DREW"
3275"DOMITILA"
3276"DOMINICA"
3277"DAINA"
3278"CREOLA"
3279"CARLI"
3280"CAMIE"
3281"BUNNY"
3282"BRITTNY"
3283"ASHANTI"
3284"ANISHA"
3285"ALEEN"
3286"ADAH"
3287"YASUKO"
3288"WINTER"
3289"VIKI"
3290"VALRIE"
3291"TONA"
3292"TINISHA"
3293"THI"
3294"TERISA"
3295"TATUM"
3296"TANEKA"
3297"SIMONNE"
3298"SHALANDA"
3299"SERITA"
3300"RESSIE"
3301"REFUGIA"
3302"PAZ"
3303"OLENE"
3304"NA"
3305"MERRILL"
3306"MARGHERITA"
3307"MANDIE"
3308"MAN"
3309"MAIRE"
3310"LYNDIA"
3311"LUCI"
3312"LORRIANE"
3313"LORETA"
3314"LEONIA"
3315"LAVONA"
3316"LASHAWNDA"
3317"LAKIA"
3318"KYOKO"
3319"KRYSTINA"
3320"KRYSTEN"
3321"KENIA"
3322"KELSI"
3323"JUDE"
3324"JEANICE"
3325"ISOBEL"
3326"GEORGIANN"
3327"GENNY"
3328"FELICIDAD"
3329"EILENE"
3330"DEON"
3331"DELOISE"
3332"DEEDEE"
3333"DANNIE"
3334"CONCEPTION"
3335"CLORA"
3336"CHERILYN"
3337"CHANG"
3338"CALANDRA"
3339"BERRY"
3340"ARMANDINA"
3341"ANISA"
3342"ULA"
3343"TIMOTHY"
3344"TIERA"
3345"THERESSA"
3346"STEPHANIA"
3347"SIMA"
3348"SHYLA"
3349"SHONTA"
3350"SHERA"
3351"SHAQUITA"
3352"SHALA"
3353"SAMMY"
3354"ROSSANA"
3355"NOHEMI"
3356"NERY"
3357"MORIAH"
3358"MELITA"
3359"MELIDA"
3360"MELANI"
3361"MARYLYNN"
3362"MARISHA"
3363"MARIETTE"
3364"MALORIE"
3365"MADELENE"
3366"LUDIVINA"
3367"LORIA"
3368"LORETTE"
3369"LORALEE"
3370"LIANNE"
3371"LEON"
3372"LAVENIA"
3373"LAURINDA"
3374"LASHON"
3375"KIT"
3376"KIMI"
3377"KEILA"
3378"KATELYNN"
3379"KAI"
3380"JONE"
3381"JOANE"
3382"JI"
3383"JAYNA"
3384"JANELLA"
3385"JA"
3386"HUE"
3387"HERTHA"
3388"FRANCENE"
3389"ELINORE"
3390"DESPINA"
3391"DELSIE"
3392"DEEDRA"
3393"CLEMENCIA"
3394"CARRY"
3395"CAROLIN"
3396"CARLOS"
3397"BULAH"
3398"BRITTANIE"
3399"BOK"
3400"BLONDELL"
3401"BIBI"
3402"BEAULAH"
3403"BEATA"
3404"ANNITA"
3405"AGRIPINA"
3406"VIRGEN"
3407"VALENE"
3408"UN"
3409"TWANDA"
3410"TOMMYE"
3411"TOI"
3412"TARRA"
3413"TARI"
3414"TAMMERA"
3415"SHAKIA"
3416"SADYE"
3417"RUTHANNE"
3418"ROCHEL"
3419"RIVKA"
3420"PURA"
3421"NENITA"
3422"NATISHA"
3423"MING"
3424"MERRILEE"
3425"MELODEE"
3426"MARVIS"
3427"LUCILLA"
3428"LEENA"
3429"LAVETA"
3430"LARITA"
3431"LANIE"
3432"KEREN"
3433"ILEEN"
3434"GEORGEANN"
3435"GENNA"
3436"GENESIS"
3437"FRIDA"
3438"EWA"
3439"EUFEMIA"
3440"EMELY"
3441"ELA"
3442"EDYTH"
3443"DEONNA"
3444"DEADRA"
3445"DARLENA"
3446"CHANELL"
3447"CHAN"
3448"CATHERN"
3449"CASSONDRA"
3450"CASSAUNDRA"
3451"BERNARDA"
3452"BERNA"
3453"ARLINDA"
3454"ANAMARIA"
3455"ALBERT"
3456"WESLEY"
3457"VERTIE"
3458"VALERI"
3459"TORRI"
3460"TATYANA"
3461"STASIA"
3462"SHERISE"
3463"SHERILL"
3464"SEASON"
3465"SCOTTIE"
3466"SANDA"
3467"RUTHE"
3468"ROSY"
3469"ROBERTO"
3470"ROBBI"
3471"RANEE"
3472"QUYEN"
3473"PEARLY"
3474"PALMIRA"
3475"ONITA"
3476"NISHA"
3477"NIESHA"
3478"NIDA"
3479"NEVADA"
3480"NAM"
3481"MERLYN"
3482"MAYOLA"
3483"MARYLOUISE"
3484"MARYLAND"
3485"MARX"
3486"MARTH"
3487"MARGENE"
3488"MADELAINE"
3489"LONDA"
3490"LEONTINE"
3491"LEOMA"
3492"LEIA"
3493"LAWRENCE"
3494"LAURALEE"
3495"LANORA"
3496"LAKITA"
3497"KIYOKO"
3498"KETURAH"
3499"KATELIN"
3500"KAREEN"
3501"JONIE"
3502"JOHNETTE"
3503"JENEE"
3504"JEANETT"
3505"IZETTA"
3506"HIEDI"
3507"HEIKE"
3508"HASSIE"
3509"HAROLD"
3510"GIUSEPPINA"
3511"GEORGANN"
3512"FIDELA"
3513"FERNANDE"
3514"ELWANDA"
3515"ELLAMAE"
3516"ELIZ"
3517"DUSTI"
3518"DOTTY"
3519"CYNDY"
3520"CORALIE"
3521"CELESTA"
3522"ARGENTINA"
3523"ALVERTA"
3524"XENIA"
3525"WAVA"
3526"VANETTA"
3527"TORRIE"
3528"TASHINA"
3529"TANDY"
3530"TAMBRA"
3531"TAMA"
3532"STEPANIE"
3533"SHILA"
3534"SHAUNTA"
3535"SHARAN"
3536"SHANIQUA"
3537"SHAE"
3538"SETSUKO"
3539"SERAFINA"
3540"SANDEE"
3541"ROSAMARIA"
3542"PRISCILA"
3543"OLINDA"
3544"NADENE"
3545"MUOI"
3546"MICHELINA"
3547"MERCEDEZ"
3548"MARYROSE"
3549"MARIN"
3550"MARCENE"
3551"MAO"
3552"MAGALI"
3553"MAFALDA"
3554"LOGAN"
3555"LINN"
3556"LANNIE"
3557"KAYCE"
3558"KAROLINE"
3559"KAMILAH"
3560"KAMALA"
3561"JUSTA"
3562"JOLINE"
3563"JENNINE"
3564"JACQUETTA"
3565"IRAIDA"
3566"GERALD"
3567"GEORGEANNA"
3568"FRANCHESCA"
3569"FAIRY"
3570"EMELINE"
3571"ELANE"
3572"EHTEL"
3573"EARLIE"
3574"DULCIE"
3575"DALENE"
3576"CRIS"
3577"CLASSIE"
3578"CHERE"
3579"CHARIS"
3580"CAROYLN"
3581"CARMINA"
3582"CARITA"
3583"BRIAN"
3584"BETHANIE"
3585"AYAKO"
3586"ARICA"
3587"AN"
3588"ALYSA"
3589"ALESSANDRA"
3590"AKILAH"
3591"ADRIEN"
3592"ZETTA"
3593"YOULANDA"
3594"YELENA"
3595"YAHAIRA"
3596"XUAN"
3597"WENDOLYN"
3598"VICTOR"
3599"TIJUANA"
3600"TERRELL"
3601"TERINA"
3602"TERESIA"
3603"SUZI"
3604"SUNDAY"
3605"SHERELL"
3606"SHAVONDA"
3607"SHAUNTE"
3608"SHARDA"
3609"SHAKITA"
3610"SENA"
3611"RYANN"
3612"RUBI"
3613"RIVA"
3614"REGINIA"
3615"REA"
3616"RACHAL"
3617"PARTHENIA"
3618"PAMULA"
3619"MONNIE"
3620"MONET"
3621"MICHAELE"
3622"MELIA"
3623"MARINE"
3624"MALKA"
3625"MAISHA"
3626"LISANDRA"
3627"LEO"
3628"LEKISHA"
3629"LEAN"
3630"LAURENCE"
3631"LAKENDRA"
3632"KRYSTIN"
3633"KORTNEY"
3634"KIZZIE"
3635"KITTIE"
3636"KERA"
3637"KENDAL"
3638"KEMBERLY"
3639"KANISHA"
3640"JULENE"
3641"JULE"
3642"JOSHUA"
3643"JOHANNE"
3644"JEFFREY"
3645"JAMEE"
3646"HAN"
3647"HALLEY"
3648"GIDGET"
3649"GALINA"
3650"FREDRICKA"
3651"FLETA"
3652"FATIMAH"
3653"EUSEBIA"
3654"ELZA"
3655"ELEONORE"
3656"DORTHEY"
3657"DORIA"
3658"DONELLA"
3659"DINORAH"
3660"DELORSE"
3661"CLARETHA"
3662"CHRISTINIA"
3663"CHARLYN"
3664"BONG"
3665"BELKIS"
3666"AZZIE"
3667"ANDERA"
3668"AIKO"
3669"ADENA"
3670"YER"
3671"YAJAIRA"
3672"WAN"
3673"VANIA"
3674"ULRIKE"
3675"TOSHIA"
3676"TIFANY"
3677"STEFANY"
3678"SHIZUE"
3679"SHENIKA"
3680"SHAWANNA"
3681"SHAROLYN"
3682"SHARILYN"
3683"SHAQUANA"
3684"SHANTAY"
3685"SEE"
3686"ROZANNE"
3687"ROSELEE"
3688"RICKIE"
3689"REMONA"
3690"REANNA"
3691"RAELENE"
3692"QUINN"
3693"PHUNG"
3694"PETRONILA"
3695"NATACHA"
3696"NANCEY"
3697"MYRL"
3698"MIYOKO"
3699"MIESHA"
3700"MERIDETH"
3701"MARVELLA"
3702"MARQUITTA"
3703"MARHTA"
3704"MARCHELLE"
3705"LIZETH"
3706"LIBBIE"
3707"LAHOMA"
3708"LADAWN"
3709"KINA"
3710"KATHELEEN"
3711"KATHARYN"
3712"KARISA"
3713"KALEIGH"
3714"JUNIE"
3715"JULIEANN"
3716"JOHNSIE"
3717"JANEAN"
3718"JAIMEE"
3719"JACKQUELINE"
3720"HISAKO"
3721"HERMA"
3722"HELAINE"
3723"GWYNETH"
3724"GLENN"
3725"GITA"
3726"EUSTOLIA"
3727"EMELINA"
3728"ELIN"
3729"EDRIS"
3730"DONNETTE"
3731"DONNETTA"
3732"DIERDRE"
3733"DENAE"
3734"DARCEL"
3735"CLAUDE"
3736"CLARISA"
3737"CINDERELLA"
3738"CHIA"
3739"CHARLESETTA"
3740"CHARITA"
3741"CELSA"
3742"CASSY"
3743"CASSI"
3744"CARLEE"
3745"BRUNA"
3746"BRITTANEY"
3747"BRANDE"
3748"BILLI"
3749"BAO"
3750"ANTONETTA"
3751"ANGLA"
3752"ANGELYN"
3753"ANALISA"
3754"ALANE"
3755"WENONA"
3756"WENDIE"
3757"VERONIQUE"
3758"VANNESA"
3759"TOBIE"
3760"TEMPIE"
3761"SUMIKO"
3762"SULEMA"
3763"SPARKLE"
3764"SOMER"
3765"SHEBA"
3766"SHAYNE"
3767"SHARICE"
3768"SHANEL"
3769"SHALON"
3770"SAGE"
3771"ROY"
3772"ROSIO"
3773"ROSELIA"
3774"RENAY"
3775"REMA"
3776"REENA"
3777"PORSCHE"
3778"PING"
3779"PEG"
3780"OZIE"
3781"ORETHA"
3782"ORALEE"
3783"ODA"
3784"NU"
3785"NGAN"
3786"NAKESHA"
3787"MILLY"
3788"MARYBELLE"
3789"MARLIN"
3790"MARIS"
3791"MARGRETT"
3792"MARAGARET"
3793"MANIE"
3794"LURLENE"
3795"LILLIA"
3796"LIESELOTTE"
3797"LAVELLE"
3798"LASHAUNDA"
3799"LAKEESHA"
3800"KEITH"
3801"KAYCEE"
3802"KALYN"
3803"JOYA"
3804"JOETTE"
3805"JENAE"
3806"JANIECE"
3807"ILLA"
3808"GRISEL"
3809"GLAYDS"
3810"GENEVIE"
3811"GALA"
3812"FREDDA"
3813"FRED"
3814"ELMER"
3815"ELEONOR"
3816"DEBERA"
3817"DEANDREA"
3818"DAN"
3819"CORRINNE"
3820"CORDIA"
3821"CONTESSA"
3822"COLENE"
3823"CLEOTILDE"
3824"CHARLOTT"
3825"CHANTAY"
3826"CECILLE"
3827"BEATRIS"
3828"AZALEE"
3829"ARLEAN"
3830"ARDATH"
3831"ANJELICA"
3832"ANJA"
3833"ALFREDIA"
3834"ALEISHA"
3835"ADAM"
3836"ZADA"
3837"YUONNE"
3838"XIAO"
3839"WILLODEAN"
3840"WHITLEY"
3841"VENNIE"
3842"VANNA"
3843"TYISHA"
3844"TOVA"
3845"TORIE"
3846"TONISHA"
3847"TILDA"
3848"TIEN"
3849"TEMPLE"
3850"SIRENA"
3851"SHERRIL"
3852"SHANTI"
3853"SHAN"
3854"SENAIDA"
3855"SAMELLA"
3856"ROBBYN"
3857"RENDA"
3858"REITA"
3859"PHEBE"
3860"PAULITA"
3861"NOBUKO"
3862"NGUYET"
3863"NEOMI"
3864"MOON"
3865"MIKAELA"
3866"MELANIA"
3867"MAXIMINA"
3868"MARG"
3869"MAISIE"
3870"LYNNA"
3871"LILLI"
3872"LAYNE"
3873"LASHAUN"
3874"LAKENYA"
3875"LAEL"
3876"KIRSTIE"
3877"KATHLINE"
3878"KASHA"
3879"KARLYN"
3880"KARIMA"
3881"JOVAN"
3882"JOSEFINE"
3883"JENNELL"
3884"JACQUI"
3885"JACKELYN"
3886"HYO"
3887"HIEN"
3888"GRAZYNA"
3889"FLORRIE"
3890"FLORIA"
3891"ELEONORA"
3892"DWANA"
3893"DORLA"
3894"DONG"
3895"DELMY"
3896"DEJA"
3897"DEDE"
3898"DANN"
3899"CRYSTA"
3900"CLELIA"
3901"CLARIS"
3902"CLARENCE"
3903"CHIEKO"
3904"CHERLYN"
3905"CHERELLE"
3906"CHARMAIN"
3907"CHARA"
3908"CAMMY"
3909"BEE"
3910"ARNETTE"
3911"ARDELLE"
3912"ANNIKA"
3913"AMIEE"
3914"AMEE"
3915"ALLENA"
3916"YVONE"
3917"YUKI"
3918"YOSHIE"
3919"YEVETTE"
3920"YAEL"
3921"WILLETTA"
3922"VONCILE"
3923"VENETTA"
3924"TULA"
3925"TONETTE"
3926"TIMIKA"
3927"TEMIKA"
3928"TELMA"
3929"TEISHA"
3930"TAREN"
3931"TA"
3932"STACEE"
3933"SHIN"
3934"SHAWNTA"
3935"SATURNINA"
3936"RICARDA"
3937"POK"
3938"PASTY"
3939"ONIE"
3940"NUBIA"
3941"MORA"
3942"MIKE"
3943"MARIELLE"
3944"MARIELLA"
3945"MARIANELA"
3946"MARDELL"
3947"MANY"
3948"LUANNA"
3949"LOISE"
3950"LISABETH"
3951"LINDSY"
3952"LILLIANA"
3953"LILLIAM"
3954"LELAH"
3955"LEIGHA"
3956"LEANORA"
3957"LANG"
3958"KRISTEEN"
3959"KHALILAH"
3960"KEELEY"
3961"KANDRA"
3962"JUNKO"
3963"JOAQUINA"
3964"JERLENE"
3965"JANI"
3966"JAMIKA"
3967"JAME"
3968"HSIU"
3969"HERMILA"
3970"GOLDEN"
3971"GENEVIVE"
3972"EVIA"
3973"EUGENA"
3974"EMMALINE"
3975"ELFREDA"
3976"ELENE"
3977"DONETTE"
3978"DELCIE"
3979"DEEANNA"
3980"DARCEY"
3981"CUC"
3982"CLARINDA"
3983"CIRA"
3984"CHAE"
3985"CELINDA"
3986"CATHERYN"
3987"CATHERIN"
3988"CASIMIRA"
3989"CARMELIA"
3990"CAMELLIA"
3991"BREANA"
3992"BOBETTE"
3993"BERNARDINA"
3994"BEBE"
3995"BASILIA"
3996"ARLYNE"
3997"AMAL"
3998"ALAYNA"
3999"ZONIA"
4000"ZENIA"
4001"YURIKO"
4002"YAEKO"
4003"WYNELL"
4004"WILLOW"
4005"WILLENA"
4006"VERNIA"
4007"TU"
4008"TRAVIS"
4009"TORA"
4010"TERRILYN"
4011"TERICA"
4012"TENESHA"
4013"TAWNA"
4014"TAJUANA"
4015"TAINA"
4016"STEPHNIE"
4017"SONA"
4018"SOL"
4019"SINA"
4020"SHONDRA"
4021"SHIZUKO"
4022"SHERLENE"
4023"SHERICE"
4024"SHARIKA"
4025"ROSSIE"
4026"ROSENA"
4027"RORY"
4028"RIMA"
4029"RIA"
4030"RHEBA"
4031"RENNA"
4032"PETER"
4033"NATALYA"
4034"NANCEE"
4035"MELODI"
4036"MEDA"
4037"MAXIMA"
4038"MATHA"
4039"MARKETTA"
4040"MARICRUZ"
4041"MARCELENE"
4042"MALVINA"
4043"LUBA"
4044"LOUETTA"
4045"LEIDA"
4046"LECIA"
4047"LAURAN"
4048"LASHAWNA"
4049"LAINE"
4050"KHADIJAH"
4051"KATERINE"
4052"KASI"
4053"KALLIE"
4054"JULIETTA"
4055"JESUSITA"
4056"JESTINE"
4057"JESSIA"
4058"JEREMY"
4059"JEFFIE"
4060"JANYCE"
4061"ISADORA"
4062"GEORGIANNE"
4063"FIDELIA"
4064"EVITA"
4065"EURA"
4066"EULAH"
4067"ESTEFANA"
4068"ELSY"
4069"ELIZABET"
4070"ELADIA"
4071"DODIE"
4072"DION"
4073"DIA"
4074"DENISSE"
4075"DELORAS"
4076"DELILA"
4077"DAYSI"
4078"DAKOTA"
4079"CURTIS"
4080"CRYSTLE"
4081"CONCHA"
4082"COLBY"
4083"CLARETTA"
4084"CHU"
4085"CHRISTIA"
4086"CHARLSIE"
4087"CHARLENA"
4088"CARYLON"
4089"BETTYANN"
4090"ASLEY"
4091"ASHLEA"
4092"AMIRA"
4093"AI"
4094"AGUEDA"
4095"AGNUS"
4096"YUETTE"
4097"VINITA"
4098"VICTORINA"
4099"TYNISHA"
4100"TREENA"
4101"TOCCARA"
4102"TISH"
4103"THOMASENA"
4104"TEGAN"
4105"SOILA"
4106"SHILOH"
4107"SHENNA"
4108"SHARMAINE"
4109"SHANTAE"
4110"SHANDI"
4111"SEPTEMBER"
4112"SARAN"
4113"SARAI"
4114"SANA"
4115"SAMUEL"
4116"SALLEY"
4117"ROSETTE"
4118"ROLANDE"
4119"REGINE"
4120"OTELIA"
4121"OSCAR"
4122"OLEVIA"
4123"NICHOLLE"
4124"NECOLE"
4125"NAIDA"
4126"MYRTA"
4127"MYESHA"
4128"MITSUE"
4129"MINTA"
4130"MERTIE"
4131"MARGY"
4132"MAHALIA"
4133"MADALENE"
4134"LOVE"
4135"LOURA"
4136"LOREAN"
4137"LEWIS"
4138"LESHA"
4139"LEONIDA"
4140"LENITA"
4141"LAVONE"
4142"LASHELL"
4143"LASHANDRA"
4144"LAMONICA"
4145"KIMBRA"
4146"KATHERINA"
4147"KARRY"
4148"KANESHA"
4149"JULIO"
4150"JONG"
4151"JENEVA"
4152"JAQUELYN"
4153"HWA"
4154"GILMA"
4155"GHISLAINE"
4156"GERTRUDIS"
4157"FRANSISCA"
4158"FERMINA"
4159"ETTIE"
4160"ETSUKO"
4161"ELLIS"
4162"ELLAN"
4163"ELIDIA"
4164"EDRA"
4165"DORETHEA"
4166"DOREATHA"
4167"DENYSE"
4168"DENNY"
4169"DEETTA"
4170"DAINE"
4171"CYRSTAL"
4172"CORRIN"
4173"CAYLA"
4174"CARLITA"
4175"CAMILA"
4176"BURMA"
4177"BULA"
4178"BUENA"
4179"BLAKE"
4180"BARABARA"
4181"AVRIL"
4182"AUSTIN"
4183"ALAINE"
4184"ZANA"
4185"WILHEMINA"
4186"WANETTA"
4187"VIRGIL"
4188"VI"
4189"VERONIKA"
4190"VERNON"
4191"VERLINE"
4192"VASILIKI"
4193"TONITA"
4194"TISA"
4195"TEOFILA"
4196"TAYNA"
4197"TAUNYA"
4198"TANDRA"
4199"TAKAKO"
4200"SUNNI"
4201"SUANNE"
4202"SIXTA"
4203"SHARELL"
4204"SEEMA"
4205"RUSSELL"
4206"ROSENDA"
4207"ROBENA"
4208"RAYMONDE"
4209"PEI"
4210"PAMILA"
4211"OZELL"
4212"NEIDA"
4213"NEELY"
4214"MISTIE"
4215"MICHA"
4216"MERISSA"
4217"MAURITA"
4218"MARYLN"
4219"MARYETTA"
4220"MARSHALL"
4221"MARCELL"
4222"MALENA"
4223"MAKEDA"
4224"MADDIE"
4225"LOVETTA"
4226"LOURIE"
4227"LORRINE"
4228"LORILEE"
4229"LESTER"
4230"LAURENA"
4231"LASHAY"
4232"LARRAINE"
4233"LAREE"
4234"LACRESHA"
4235"KRISTLE"
4236"KRISHNA"
4237"KEVA"
4238"KEIRA"
4239"KAROLE"
4240"JOIE"
4241"JINNY"
4242"JEANNETTA"
4243"JAMA"
4244"HEIDY"
4245"GILBERTE"
4246"GEMA"
4247"FAVIOLA"
4248"EVELYNN"
4249"ENDA"
4250"ELLI"
4251"ELLENA"
4252"DIVINA"
4253"DAGNY"
4254"COLLENE"
4255"CODI"
4256"CINDIE"
4257"CHASSIDY"
4258"CHASIDY"
4259"CATRICE"
4260"CATHERINA"
4261"CASSEY"
4262"CAROLL"
4263"CARLENA"
4264"CANDRA"
4265"CALISTA"
4266"BRYANNA"
4267"BRITTENY"
4268"BEULA"
4269"BARI"
4270"AUDRIE"
4271"AUDRIA"
4272"ARDELIA"
4273"ANNELLE"
4274"ANGILA"
4275"ALONA"
4276"ALLYN"
4277"DOUGLAS"
4278"ROGER"
4279"JONATHAN"
4280"RALPH"
4281"NICHOLAS"
4282"BENJAMIN"
4283"BRUCE"
4284"HARRY"
4285"WAYNE"
4286"STEVE"
4287"HOWARD"
4288"ERNEST"
4289"PHILLIP"
4290"TODD"
4291"CRAIG"
4292"ALAN"
4293"PHILIP"
4294"EARL"
4295"DANNY"
4296"BRYAN"
4297"STANLEY"
4298"LEONARD"
4299"NATHAN"
4300"MANUEL"
4301"RODNEY"
4302"MARVIN"
4303"VINCENT"
4304"JEFFERY"
4305"JEFF"
4306"CHAD"
4307"JACOB"
4308"ALFRED"
4309"BRADLEY"
4310"HERBERT"
4311"FREDERICK"
4312"EDWIN"
4313"DON"
4314"RICKY"
4315"RANDALL"
4316"BARRY"
4317"BERNARD"
4318"LEROY"
4319"MARCUS"
4320"THEODORE"
4321"CLIFFORD"
4322"MIGUEL"
4323"JIM"
4324"TOM"
4325"CALVIN"
4326"BILL"
4327"LLOYD"
4328"DEREK"
4329"WARREN"
4330"DARRELL"
4331"JEROME"
4332"FLOYD"
4333"ALVIN"
4334"TIM"
4335"GORDON"
4336"GREG"
4337"JORGE"
4338"DUSTIN"
4339"PEDRO"
4340"DERRICK"
4341"ZACHARY"
4342"HERMAN"
4343"GLEN"
4344"HECTOR"
4345"RICARDO"
4346"RICK"
4347"BRENT"
4348"RAMON"
4349"GILBERT"
4350"MARC"
4351"REGINALD"
4352"RUBEN"
4353"NATHANIEL"
4354"RAFAEL"
4355"EDGAR"
4356"MILTON"
4357"RAUL"
4358"BEN"
4359"CHESTER"
4360"DUANE"
4361"FRANKLIN"
4362"BRAD"
4363"RON"
4364"ROLAND"
4365"ARNOLD"
4366"HARVEY"
4367"JARED"
4368"ERIK"
4369"DARRYL"
4370"NEIL"
4371"JAVIER"
4372"FERNANDO"
4373"CLINTON"
4374"TED"
4375"MATHEW"
4376"TYRONE"
4377"DARREN"
4378"LANCE"
4379"KURT"
4380"ALLAN"
4381"NELSON"
4382"GUY"
4383"CLAYTON"
4384"HUGH"
4385"MAX"
4386"DWAYNE"
4387"DWIGHT"
4388"ARMANDO"
4389"FELIX"
4390"EVERETT"
4391"IAN"
4392"WALLACE"
4393"KEN"
4394"BOB"
4395"ALFREDO"
4396"ALBERTO"
4397"DAVE"
4398"IVAN"
4399"BYRON"
4400"ISAAC"
4401"MORRIS"
4402"CLIFTON"
4403"WILLARD"
4404"ROSS"
4405"ANDY"
4406"SALVADOR"
4407"KIRK"
4408"SERGIO"
4409"SETH"
4410"KENT"
4411"TERRANCE"
4412"EDUARDO"
4413"TERRENCE"
4414"ENRIQUE"
4415"WADE"
4416"STUART"
4417"FREDRICK"
4418"ARTURO"
4419"ALEJANDRO"
4420"NICK"
4421"LUTHER"
4422"WENDELL"
4423"JEREMIAH"
4424"JULIUS"
4425"OTIS"
4426"TREVOR"
4427"OLIVER"
4428"LUKE"
4429"HOMER"
4430"GERARD"
4431"DOUG"
4432"KENNY"
4433"HUBERT"
4434"LYLE"
4435"MATT"
4436"ALFONSO"
4437"ORLANDO"
4438"REX"
4439"CARLTON"
4440"ERNESTO"
4441"NEAL"
4442"PABLO"
4443"LORENZO"
4444"OMAR"
4445"WILBUR"
4446"GRANT"
4447"HORACE"
4448"RODERICK"
4449"ABRAHAM"
4450"WILLIS"
4451"RICKEY"
4452"ANDRES"
4453"CESAR"
4454"JOHNATHAN"
4455"MALCOLM"
4456"RUDOLPH"
4457"DAMON"
4458"KELVIN"
4459"PRESTON"
4460"ALTON"
4461"ARCHIE"
4462"MARCO"
4463"WM"
4464"PETE"
4465"RANDOLPH"
4466"GARRY"
4467"GEOFFREY"
4468"JONATHON"
4469"FELIPE"
4470"GERARDO"
4471"ED"
4472"DOMINIC"
4473"DELBERT"
4474"COLIN"
4475"GUILLERMO"
4476"EARNEST"
4477"LUCAS"
4478"BENNY"
4479"SPENCER"
4480"RODOLFO"
4481"MYRON"
4482"EDMUND"
4483"GARRETT"
4484"SALVATORE"
4485"CEDRIC"
4486"LOWELL"
4487"GREGG"
4488"SHERMAN"
4489"WILSON"
4490"SYLVESTER"
4491"ROOSEVELT"
4492"ISRAEL"
4493"JERMAINE"
4494"FORREST"
4495"WILBERT"
4496"LELAND"
4497"SIMON"
4498"CLARK"
4499"IRVING"
4500"BRYANT"
4501"OWEN"
4502"RUFUS"
4503"WOODROW"
4504"KRISTOPHER"
4505"MACK"
4506"LEVI"
4507"MARCOS"
4508"GUSTAVO"
4509"JAKE"
4510"LIONEL"
4511"GILBERTO"
4512"CLINT"
4513"NICOLAS"
4514"ISMAEL"
4515"ORVILLE"
4516"ERVIN"
4517"DEWEY"
4518"AL"
4519"WILFRED"
4520"JOSH"
4521"HUGO"
4522"IGNACIO"
4523"CALEB"
4524"TOMAS"
4525"SHELDON"
4526"ERICK"
4527"STEWART"
4528"DOYLE"
4529"DARREL"
4530"ROGELIO"
4531"TERENCE"
4532"SANTIAGO"
4533"ALONZO"
4534"ELIAS"
4535"BERT"
4536"ELBERT"
4537"RAMIRO"
4538"CONRAD"
4539"NOAH"
4540"GRADY"
4541"PHIL"
4542"CORNELIUS"
4543"LAMAR"
4544"ROLANDO"
4545"CLAY"
4546"PERCY"
4547"DEXTER"
4548"BRADFORD"
4549"DARIN"
4550"AMOS"
4551"MOSES"
4552"IRVIN"
4553"SAUL"
4554"ROMAN"
4555"RANDAL"
4556"TIMMY"
4557"DARRIN"
4558"WINSTON"
4559"BRENDAN"
4560"ABEL"
4561"DOMINICK"
4562"BOYD"
4563"EMILIO"
4564"ELIJAH"
4565"DOMINGO"
4566"EMMETT"
4567"MARLON"
4568"EMANUEL"
4569"JERALD"
4570"EDMOND"
4571"EMIL"
4572"DEWAYNE"
4573"WILL"
4574"OTTO"
4575"TEDDY"
4576"REYNALDO"
4577"BRET"
4578"JESS"
4579"TRENT"
4580"HUMBERTO"
4581"EMMANUEL"
4582"STEPHAN"
4583"VICENTE"
4584"LAMONT"
4585"GARLAND"
4586"MILES"
4587"EFRAIN"
4588"HEATH"
4589"RODGER"
4590"HARLEY"
4591"ETHAN"
4592"ELDON"
4593"ROCKY"
4594"PIERRE"
4595"JUNIOR"
4596"FREDDY"
4597"ELI"
4598"BRYCE"
4599"ANTOINE"
4600"STERLING"
4601"CHASE"
4602"GROVER"
4603"ELTON"
4604"CLEVELAND"
4605"DYLAN"
4606"CHUCK"
4607"DAMIAN"
4608"REUBEN"
4609"STAN"
4610"AUGUST"
4611"LEONARDO"
4612"JASPER"
4613"RUSSEL"
4614"ERWIN"
4615"BENITO"
4616"HANS"
4617"MONTE"
4618"BLAINE"
4619"ERNIE"
4620"CURT"
4621"QUENTIN"
4622"AGUSTIN"
4623"MURRAY"
4624"JAMAL"
4625"ADOLFO"
4626"HARRISON"
4627"TYSON"
4628"BURTON"
4629"BRADY"
4630"ELLIOTT"
4631"WILFREDO"
4632"BART"
4633"JARROD"
4634"VANCE"
4635"DENIS"
4636"DAMIEN"
4637"JOAQUIN"
4638"HARLAN"
4639"DESMOND"
4640"ELLIOT"
4641"DARWIN"
4642"GREGORIO"
4643"BUDDY"
4644"XAVIER"
4645"KERMIT"
4646"ROSCOE"
4647"ESTEBAN"
4648"ANTON"
4649"SOLOMON"
4650"SCOTTY"
4651"NORBERT"
4652"ELVIN"
4653"WILLIAMS"
4654"NOLAN"
4655"ROD"
4656"QUINTON"
4657"HAL"
4658"BRAIN"
4659"ROB"
4660"ELWOOD"
4661"KENDRICK"
4662"DARIUS"
4663"MOISES"
4664"FIDEL"
4665"THADDEUS"
4666"CLIFF"
4667"MARCEL"
4668"JACKSON"
4669"RAPHAEL"
4670"BRYON"
4671"ARMAND"
4672"ALVARO"
4673"JEFFRY"
4674"DANE"
4675"JOESPH"
4676"THURMAN"
4677"NED"
4678"RUSTY"
4679"MONTY"
4680"FABIAN"
4681"REGGIE"
4682"MASON"
4683"GRAHAM"
4684"ISAIAH"
4685"VAUGHN"
4686"GUS"
4687"LOYD"
4688"DIEGO"
4689"ADOLPH"
4690"NORRIS"
4691"MILLARD"
4692"ROCCO"
4693"GONZALO"
4694"DERICK"
4695"RODRIGO"
4696"WILEY"
4697"RIGOBERTO"
4698"ALPHONSO"
4699"TY"
4700"NOE"
4701"VERN"
4702"REED"
4703"JEFFERSON"
4704"ELVIS"
4705"BERNARDO"
4706"MAURICIO"
4707"HIRAM"
4708"DONOVAN"
4709"BASIL"
4710"RILEY"
4711"NICKOLAS"
4712"MAYNARD"
4713"SCOT"
4714"VINCE"
4715"QUINCY"
4716"EDDY"
4717"SEBASTIAN"
4718"FEDERICO"
4719"ULYSSES"
4720"HERIBERTO"
4721"DONNELL"
4722"COLE"
4723"DAVIS"
4724"GAVIN"
4725"EMERY"
4726"WARD"
4727"ROMEO"
4728"JAYSON"
4729"DANTE"
4730"CLEMENT"
4731"COY"
4732"MAXWELL"
4733"JARVIS"
4734"BRUNO"
4735"ISSAC"
4736"DUDLEY"
4737"BROCK"
4738"SANFORD"
4739"CARMELO"
4740"BARNEY"
4741"NESTOR"
4742"STEFAN"
4743"DONNY"
4744"ART"
4745"LINWOOD"
4746"BEAU"
4747"WELDON"
4748"GALEN"
4749"ISIDRO"
4750"TRUMAN"
4751"DELMAR"
4752"JOHNATHON"
4753"SILAS"
4754"FREDERIC"
4755"DICK"
4756"IRWIN"
4757"MERLIN"
4758"CHARLEY"
4759"MARCELINO"
4760"HARRIS"
4761"CARLO"
4762"TRENTON"
4763"KURTIS"
4764"HUNTER"
4765"AURELIO"
4766"WINFRED"
4767"VITO"
4768"COLLIN"
4769"DENVER"
4770"CARTER"
4771"LEONEL"
4772"EMORY"
4773"PASQUALE"
4774"MOHAMMAD"
4775"MARIANO"
4776"DANIAL"
4777"LANDON"
4778"DIRK"
4779"BRANDEN"
4780"ADAN"
4781"BUFORD"
4782"GERMAN"
4783"WILMER"
4784"EMERSON"
4785"ZACHERY"
4786"FLETCHER"
4787"JACQUES"
4788"ERROL"
4789"DALTON"
4790"MONROE"
4791"JOSUE"
4792"EDWARDO"
4793"BOOKER"
4794"WILFORD"
4795"SONNY"
4796"SHELTON"
4797"CARSON"
4798"THERON"
4799"RAYMUNDO"
4800"DAREN"
4801"HOUSTON"
4802"ROBBY"
4803"LINCOLN"
4804"GENARO"
4805"BENNETT"
4806"OCTAVIO"
4807"CORNELL"
4808"HUNG"
4809"ARRON"
4810"ANTONY"
4811"HERSCHEL"
4812"GIOVANNI"
4813"GARTH"
4814"CYRUS"
4815"CYRIL"
4816"RONNY"
4817"LON"
4818"FREEMAN"
4819"DUNCAN"
4820"KENNITH"
4821"CARMINE"
4822"ERICH"
4823"CHADWICK"
4824"WILBURN"
4825"RUSS"
4826"REID"
4827"MYLES"
4828"ANDERSON"
4829"MORTON"
4830"JONAS"
4831"FOREST"
4832"MITCHEL"
4833"MERVIN"
4834"ZANE"
4835"RICH"
4836"JAMEL"
4837"LAZARO"
4838"ALPHONSE"
4839"RANDELL"
4840"MAJOR"
4841"JARRETT"
4842"BROOKS"
4843"ABDUL"
4844"LUCIANO"
4845"SEYMOUR"
4846"EUGENIO"
4847"MOHAMMED"
4848"VALENTIN"
4849"CHANCE"
4850"ARNULFO"
4851"LUCIEN"
4852"FERDINAND"
4853"THAD"
4854"EZRA"
4855"ALDO"
4856"RUBIN"
4857"ROYAL"
4858"MITCH"
4859"EARLE"
4860"ABE"
4861"WYATT"
4862"MARQUIS"
4863"LANNY"
4864"KAREEM"
4865"JAMAR"
4866"BORIS"
4867"ISIAH"
4868"EMILE"
4869"ELMO"
4870"ARON"
4871"LEOPOLDO"
4872"EVERETTE"
4873"JOSEF"
4874"ELOY"
4875"RODRICK"
4876"REINALDO"
4877"LUCIO"
4878"JERROD"
4879"WESTON"
4880"HERSHEL"
4881"BARTON"
4882"PARKER"
4883"LEMUEL"
4884"BURT"
4885"JULES"
4886"GIL"
4887"ELISEO"
4888"AHMAD"
4889"NIGEL"
4890"EFREN"
4891"ANTWAN"
4892"ALDEN"
4893"MARGARITO"
4894"COLEMAN"
4895"DINO"
4896"OSVALDO"
4897"LES"
4898"DEANDRE"
4899"NORMAND"
4900"KIETH"
4901"TREY"
4902"NORBERTO"
4903"NAPOLEON"
4904"JEROLD"
4905"FRITZ"
4906"ROSENDO"
4907"MILFORD"
4908"CHRISTOPER"
4909"ALFONZO"
4910"LYMAN"
4911"JOSIAH"
4912"BRANT"
4913"WILTON"
4914"RICO"
4915"JAMAAL"
4916"DEWITT"
4917"BRENTON"
4918"OLIN"
4919"FOSTER"
4920"FAUSTINO"
4921"CLAUDIO"
4922"JUDSON"
4923"GINO"
4924"EDGARDO"
4925"ALEC"
4926"TANNER"
4927"JARRED"
4928"DONN"
4929"TAD"
4930"PRINCE"
4931"PORFIRIO"
4932"ODIS"
4933"LENARD"
4934"CHAUNCEY"
4935"TOD"
4936"MEL"
4937"MARCELO"
4938"KORY"
4939"AUGUSTUS"
4940"KEVEN"
4941"HILARIO"
4942"BUD"
4943"SAL"
4944"ORVAL"
4945"MAURO"
4946"ZACHARIAH"
4947"OLEN"
4948"ANIBAL"
4949"MILO"
4950"JED"
4951"DILLON"
4952"AMADO"
4953"NEWTON"
4954"LENNY"
4955"RICHIE"
4956"HORACIO"
4957"BRICE"
4958"MOHAMED"
4959"DELMER"
4960"DARIO"
4961"REYES"
4962"MAC"
4963"JONAH"
4964"JERROLD"
4965"ROBT"
4966"HANK"
4967"RUPERT"
4968"ROLLAND"
4969"KENTON"
4970"DAMION"
4971"ANTONE"
4972"WALDO"
4973"FREDRIC"
4974"BRADLY"
4975"KIP"
4976"BURL"
4977"WALKER"
4978"TYREE"
4979"JEFFEREY"
4980"AHMED"
4981"WILLY"
4982"STANFORD"
4983"OREN"
4984"NOBLE"
4985"MOSHE"
4986"MIKEL"
4987"ENOCH"
4988"BRENDON"
4989"QUINTIN"
4990"JAMISON"
4991"FLORENCIO"
4992"DARRICK"
4993"TOBIAS"
4994"HASSAN"
4995"GIUSEPPE"
4996"DEMARCUS"
4997"CLETUS"
4998"TYRELL"
4999"LYNDON"
5000"KEENAN"
5001"WERNER"
5002"GERALDO"
5003"COLUMBUS"
5004"CHET"
5005"BERTRAM"
5006"MARKUS"
5007"HUEY"
5008"HILTON"
5009"DWAIN"
5010"DONTE"
5011"TYRON"
5012"OMER"
5013"ISAIAS"
5014"HIPOLITO"
5015"FERMIN"
5016"ADALBERTO"
5017"BO"
5018"BARRETT"
5019"TEODORO"
5020"MCKINLEY"
5021"MAXIMO"
5022"GARFIELD"
5023"RALEIGH"
5024"LAWERENCE"
5025"ABRAM"
5026"RASHAD"
5027"KING"
5028"EMMITT"
5029"DARON"
5030"SAMUAL"
5031"MIQUEL"
5032"EUSEBIO"
5033"DOMENIC"
5034"DARRON"
5035"BUSTER"
5036"WILBER"
5037"RENATO"
5038"JC"
5039"HOYT"
5040"HAYWOOD"
5041"EZEKIEL"
5042"CHAS"
5043"FLORENTINO"
5044"ELROY"
5045"CLEMENTE"
5046"ARDEN"
5047"NEVILLE"
5048"EDISON"
5049"DESHAWN"
5050"NATHANIAL"
5051"JORDON"
5052"DANILO"
5053"CLAUD"
5054"SHERWOOD"
5055"RAYMON"
5056"RAYFORD"
5057"CRISTOBAL"
5058"AMBROSE"
5059"TITUS"
5060"HYMAN"
5061"FELTON"
5062"EZEQUIEL"
5063"ERASMO"
5064"STANTON"
5065"LONNY"
5066"LEN"
5067"IKE"
5068"MILAN"
5069"LINO"
5070"JAROD"
5071"HERB"
5072"ANDREAS"
5073"WALTON"
5074"RHETT"
5075"PALMER"
5076"DOUGLASS"
5077"CORDELL"
5078"OSWALDO"
5079"ELLSWORTH"
5080"VIRGILIO"
5081"TONEY"
5082"NATHANAEL"
5083"DEL"
5084"BENEDICT"
5085"MOSE"
5086"JOHNSON"
5087"ISREAL"
5088"GARRET"
5089"FAUSTO"
5090"ASA"
5091"ARLEN"
5092"ZACK"
5093"WARNER"
5094"MODESTO"
5095"FRANCESCO"
5096"MANUAL"
5097"GAYLORD"
5098"GASTON"
5099"FILIBERTO"
5100"DEANGELO"
5101"MICHALE"
5102"GRANVILLE"
5103"WES"
5104"MALIK"
5105"ZACKARY"
5106"TUAN"
5107"ELDRIDGE"
5108"CRISTOPHER"
5109"CORTEZ"
5110"ANTIONE"
5111"MALCOM"
5112"LONG"
5113"KOREY"
5114"JOSPEH"
5115"COLTON"
5116"WAYLON"
5117"VON"
5118"HOSEA"
5119"SHAD"
5120"SANTO"
5121"RUDOLF"
5122"ROLF"
5123"REY"
5124"RENALDO"
5125"MARCELLUS"
5126"LUCIUS"
5127"KRISTOFER"
5128"BOYCE"
5129"BENTON"
5130"HAYDEN"
5131"HARLAND"
5132"ARNOLDO"
5133"RUEBEN"
5134"LEANDRO"
5135"KRAIG"
5136"JERRELL"
5137"JEROMY"
5138"HOBERT"
5139"CEDRICK"
5140"ARLIE"
5141"WINFORD"
5142"WALLY"
5143"LUIGI"
5144"KENETH"
5145"JACINTO"
5146"GRAIG"
5147"FRANKLYN"
5148"EDMUNDO"
5149"SID"
5150"PORTER"
5151"LEIF"
5152"JERAMY"
5153"BUCK"
5154"WILLIAN"
5155"VINCENZO"
5156"SHON"
5157"LYNWOOD"
5158"JERE"
5159"HAI"
5160"ELDEN"
5161"DORSEY"
5162"DARELL"
5163"BRODERICK"
5164"ALONSO"
5165))
5166
5167;;destructive sort. sort is a bit confusing, look it up!
5168(setq pe-22-names-sorted (sort pe-22-names 'string<))
5169(car pe-22-names-sorted);AARON
5170;; (let ((s "COLIN")) (cl-loop for i from 0 to (1- (length s)) sum (- (aref s i) ?A -1))) = 53
5171
5172(defun pe-sum-string (s)
5173  (cl-loop for i from 0 to (1- (length s)) sum (- (aref s i) ?A -1))
5174  )
5175(pe-sum-string "COLIN") ;53
5176
5177(defun pe-22 (names)
5178  (cl-loop for i from 0 to ( length names)
5179	   sum (* (1+ i) (pe-sum-string (nth i names))))
5180
5181  )
5182(pe-22 pe-22-names-sorted)

TODO 23: Non-abundant sums

A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.

A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.

As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

A

The brute approach seems to be:

  • find all abundant numbers up to 28123
  • test every number up to 28123 and see if they can be formed as a sum of a pair of abundant numbers

again, use pe-divisors.

 1(defun pe-23-abundantp (n)
 2  (let ((divsum (apply '+  (delq n (pe-divisors n))) ))
 3
 4    (if (> divsum n) t nil))
 5
 6  )
 7
 8(pe-23-abundantp 12)
 9(pe-23-abundantp 11)
10
11(defun pe-23-abundant-numbers (limit)
12  (cl-loop for n from 1 to limit
13	   when (pe-23-abundantp n)
14	   collect n))
15
16;;too slow, probably because pe-divisors too slow
17(pe-23-abundant-numbers 28123)

DONE 24: Lexicographic permutations

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

A

feels like a binary counter where each digit has identity. so, a hex counter perhaps. it should be possible to just count and then map the number. or, just brute force with array swapping about.

some googling reveals this is an job for Dijkstras Permutation algorithm. "A Discipline of Programming", p71.

 1
 2
 3(defun pe-24-get-next (a)
 4  (let* ((N (length a))
 5	 (i (1- N))
 6	 (j N)
 7	 (tmp))
 8
 9    (while (>= (aref a (1- i)) (aref a i))
10      (setq i (1- i)))
11
12    (while (<= (aref a (1- j)) (aref a (1- i)))
13      (setq j (1- j)))
14
15    (setq tmp (aref a (1- i)))
16    (aset a (1- i) (aref a (1- j)))
17    (aset a (1- j) tmp)
18
19    (setq i (1+ i))
20    (setq j N)
21
22    (while (< i j)
23      (setq tmp (aref a (1- i)))
24      (aset a (1- i) (aref a (1- j)))
25      (aset a (1- j) tmp)
26      (setq i (1+ i))
27      (setq j (1- j))
28
29      )
30
31    a)
32
33  )
34
35(setq pe-24-tst '[0 1 2])
36(pe-24-get-next pe-24-tst )
37(pe-24-get-next pe-24-tst )
38(pe-24-get-next pe-24-tst )
39
40(setq pe-24-data '[0 1 2 3 4 5 6 7 8 9])
41
42(cl-loop for i from 2 to 1000000 do
43	 (pe-24-get-next pe-24-data ))
44[2 7 8 3 9 1 5 4 6 0]

DONE 25: 1000-digit Fibonacci number US

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be:

F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144 The 12th term, F12, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

A

 1    ;;fibonaccio
 2
 3    ;;(let ((a 1)(b 2) (c 0)) (cl-loop for x from 1 to 7 do  (setq c (+ a b) a b b c)   ) (list a b c))
 4
 5
 6(let ((a 1)
 7      (b 2)
 8      (c 0))
 9  (cl-loop for x from 1 to 5000  do
10	   (setq c (calcFunc-add a b) a b b c)
11	   collect (list x (length  (math-format-number a)) (math-format-number a)) ))

the program returns a list of entries like: (4782 1000 "2801469855604761894059409930976292608793189978672012451535011405345311945794696621442398694512310055716262670442896176725381946499178066837020390774561243726189436148701290012421378734474935318536968012744863651325335424749327926920635103924103592765660586769954373026421114178654129286781210498785998978389309747942791704071154402549794489499148274933211656028171413521014052342726162889790023344651116069165442334492680160832967277887876571406187091478251127403655836899164772664844669221130648992221561852605690167911104874474356129833642614490064356903074834574084595401004358914796744954081860965752078260636587113228959995092232938638814540894633844779478789840107841323109156931242427255030565305331981918377443026714031086196370948154624681729367295927223995614031187833101306567470907219730384018653937477869618131642237399576685620704962738456722775917892775149556342671449194546543491060300071014852004881799935479347159713061656155381249895378355070405844736166089345030856113906348616613") sequence, length, and the fibbonacio number.

the solution uses bignums and strings, but is pretty fast even so!

DONE 27: Quadratic primes TT

Euler discovered the remarkable quadratic formula:

n² + n + 41

It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.

The incredible formula n² − 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, −79 and 1601, is −126479.

Considering quadratics of the form:

n² + an + b, where |a| < 1000 and |b| < 1000

where |n| is the modulus/absolute value of n e.g. |11| = 11 and |−4| = 4

Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0.

A

 1;;try the given formulas 1st
 2;;n² + n + 41
 3(cl-loop for n from 1 to 40 collect (+ (expt n 2) n 41))
 4(43 47 53 61 71 83 97 113 131 151 173 197 223 251 281 313 347 383 421 461 503 547 593 641 691 743 797 853 911 971 1033 1097 1163 1231 1301 1373 1447 1523 1601 1681)
 5;; n² − 79n + 1601
 6(cl-loop for n from 1 to 79 collect (+ (expt n 2) (* 79 n) 1601))(1681 1763 1847 1933 2021 2111 2203 2297 2393 2491 2591 2693 2797 2903 3011 3121 3233 3347 3463 3581 3701 3823 3947 4073 4201 4331 4463 4597 4733 4871 5011 5153 5297 5443 5591 5741 5893 6047 6203 6361 6521 6683 6847 7013 7181 7351 7523 7697 7873 8051 8231 8413 8597 8783 8971 9161 9353 9547 9743 9941 10141 10343 10547 10753 10961 11171 11383 11597 11813 12031 12251 12473 12697 12923 13151 13381 13613 13847 14083)
 7
 8;;the naive brute force approach;
 9;;theres a primep in bbdb as well, it turns out, but its not correct for negative numbers
10(defun pe-27 (maxa maxb)
11  (let (rv tmp)
12    (cl-loop for a from (* -1 maxa) to maxa collect
13	     (cl-loop for b from (* -1 maxb) to maxb do
14		      (setq tmp (cl-loop for n from 1 to 1000 ;;we should finish rather more quickly
15					 for primecandidate = (+ (expt n 2) (* a n) b)
16					 until (not (primep primecandidate))
17					 collect  primecandidate))
18		      (if (>  (length  tmp) 20) (setq rv
19						 (append  rv  (list a b (* a b)': tmp))))
20		      )) rv))
21
22(pe-27 50 50)
23
24(pe-27 999 999)
25;;the winning sequence:
26;;-61 971 -59231 :
27;;     (911 853 797 743 691 641 593 547 503 461 421 383 347 313 281 251 223 197 173 151 131 113 97 83 71 61 53 47 43 41 41 43 47 53 61 71 83 97 113 131 151 173 197 223 251 281 313 347 383 421 461 503 547 593 641 691 743 797 853 911 971 1033 1097 1163 1231 1301 1373 1447 1523 1601)

DONE 28: Number spiral diagonals

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

A

a spiral can be drawn by a turtle travelling from the center outwards with these increments: E: 1,0 S: 0,1 W: -1,0 N: 0,-1 then you begin again from E. switch increments at 1,1,2,2,3,3,4,4,...

 1
 2(defun pe-turtle (curxinc curyinc)
 3  (cond ( (and (= 1 curxinc)(= 0 curyinc))
 4	    '(0 1))
 5	( (and (= 0 curxinc)(= 1 curyinc))
 6	  '(-1 0))
 7	( (and (= -1 curxinc)(= 0 curyinc))
 8	  '(0 -1))
 9	( (and (= 0 curxinc)(= -1 curyinc))
10	  '(1 0))
11	))
12
13(defun pe-make-spiral (matrix)
14  (let* ((curxinc 1)
15	(curyinc 0)
16	(ml (length matrix))
17	(x (1+  (/ ml 2)))
18	(y x)
19	( nextinc)
20	(seglength 1)
21	(i 1))
22    (cl-loop for turn-outer from 1 to ml do
23	     (cl-loop for turn-inner from 1 to 2 do
24		      (cl-loop for segstep from 1 to seglength
25			       until (= i (1+  (* ml ml))) do
26		       ;;        (message "X:%d Y:%d I:%d" x y i)
27			       (aset (aref  matrix (1-  y)) (1-  x) i)
28			       (setq i (1+ i))
29			       (setq x (+ x curxinc))
30			       (setq y (+ y curyinc))
31			       )
32		      (setq nextinc (pe-turtle curxinc curyinc))
33		      (setq curxinc (car nextinc)
34			    curyinc (cadr nextinc))
35		      )
36	     (setq seglength (1+ seglength))))
37  matrix)
38
39;;(make-vector 5 (make-vector 5 0)); this funnily doesnt work, because the 2nd make-vector isnt copied, just its pointer is copied.
40;;obvious in retrospect
41(pe-make-spiral
42 [[0 0 0 0 0 ]
43 [0 0 0 0 0]
44 [0 0 0 0 0]
45 [0 0 0 0 0]
46 [0 0 0 0 0]])
47
48(length  [[21 22 23 24 25] [20 7 8 9 10] [19 6 1 2 11] [18 5 4 3 12] [17 16 15 14 13]])
49
50(pe-make-spiral
51 (let (matrix) (cl-loop for i from 1 to 11 do (setq matrix (vconcat matrix (make-vector 1(make-vector 11 0)) ))) matrix))
52
53(defun pe-grid-slice-vec (grid x y length direction)
54  (let (( xinc 0) ( yinc 0) (rv))
55    (cond ((eq 'S direction) (setq yinc 1))
56	  ((eq 'E direction) (setq xinc 1))
57	  ((eq 'SE direction) (setq xinc 1)(setq yinc 1))
58	  ((eq 'SW direction) (setq xinc -1)(setq yinc 1))
59	  ((eq 'NE direction) (setq xinc 1)(setq yinc -1))
60	  )
61    (cl-loop for i from 1 to length do
62	     (setq rv (cons (aref  (aref  grid y) x) rv))
63	     (setq x (+ x xinc))
64	     (setq y (+ y yinc)))
65    rv
66    )
67  )
68
69(pe-grid-slice-vec  [[21 22 23 24 25] [20 7 8 9 10] [19 6 1 2 11] [18 5 4 3 12] [17 16 15 14 13]] 0 4 5 'NE)
70
71(defun pe-sum-diagonals (size)
72  (let ( (matrix))
73    (cl-loop for i from 1 to size do (setq matrix (vconcat matrix (make-vector 1(make-vector size 0)) )))
74    (pe-make-spiral matrix)
75    (1- ;;dont count the center twice
76     (+
77      (apply '+ (pe-grid-slice-vec matrix 0 0 size 'SE))
78      (apply '+ (pe-grid-slice-vec matrix 0 (1- size) size 'NE))))
79    ))
80
81(pe-sum-diagonals 5)
82101
83
84(pe-sum-diagonals 1001)
85669171001

DONE 29: Distinct powers

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=3125 If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

A

 1  (defun pe-29 (max)
 2    (sort (cl-loop for a from 2 to max append
 3		   (cl-loop for b from 2 to max collect
 4			    (calcFunc-pow a b)))
 5	  'calcFunc-lt
 6	  )
 7    )
 8
 9  (pe-29 5)
10  (4 8 9 16 16 25 27 32 64 81 125 243 256 625 1024 3125)
11
12(length (delete-dups (pe-29 100))) 9183

the solution is kind of slow, but its fun watching the bignums grow!

DONE 30: Digit fifth powers

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 1^4 + 6^4 + 3^4 + 4^4 8208 = 8^4 + 2^4 + 0^4 + 8^4 9474 = 9^4 + 4^4 + 7^4 + 4^4 As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

A

seems similar to 34, where you also had to chop up numbers and sum them, but in that case factorial.

Finding the upper bound wasnt immediately obvious, just like PE34.

9^5 = 59049, so we need at least 6 digits.

(* 6 (expt 9 5)) is 354294.

 1;;almost identical to pe34, so could be refactored
 2(defun pe-30-powsum (n power)
 3  (let ((rv 0))
 4    (while (> n 0)
 5      (setq rv (+ rv (expt (mod n 10) power)))
 6      (setq n (/ n 10)))
 7    rv))
 8;;tests
 9(= 1634 (pe-30-powsum 1634 4))
10(= 8208 (pe-30-powsum 8208 4))
11(/= 8209 (pe-30-powsum 8209 4))
12
13
14(defun pe-30 ()
15    (let ((limit  (* 6 (expt 9 5)))) ;;the upper bound was meditated upon
16      (cl-loop for n from 2 to limit ;;no 1
17	       for powsum = (pe-30-powsum n 5)
18	       when (= powsum n)
19	       sum powsum)))
20
21(=  (pe-30) 443839)

TODO 32: Pandigital products PI

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

A

DONE 34: Digit factorials FF

Problem 34 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as 1! = 1 and 2! = 2 are not sums they are not included.

A

the upper bound is (* 7 (calcFunc-fact 9)) 2540160. 2540160 has 7 digits. (* 8 (calcFunc-fact 9)) 2903040 has also 7 digits, so the sum of the digits factorials can never become a 8 digit number.

just to make sure, (* 100 (calcFunc-fact 9)) 36288000, has nowhere near 100 digits!

so now its just brute force to the upper bound!

 1;;this factsum would be nicer as recursive
 2;;perhaps would be faster with memoization of fact, since we only need 9 values
 3  (defun pe-34-factsum (n)
 4    (let ((rv 0))
 5      (while (> n 0)
 6	(setq rv (+ rv (calcFunc-fact (mod n 10))))
 7	(setq n (/ n 10))
 8	)
 9      rv)
10    )
11  (pe-34-factsum 145); 145, so okay!
12
13  (defun pe-34 ()
14    (let ((limit  (* 7 (calcFunc-fact 9))))
15      (cl-loop for n from 3 to limit ;;fact 1 and 2 shouldnt be added according to specs
16	       for nfactsum = (pe-34-factsum n)
17	       when (= nfactsum n)
18	       sum nfactsum)))
19
20  (pe-34)
21  40730

TODO 35: Circular primes PI

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?

TODO 36: Double-base palindromes US

The decimal number, 585 = 10010010012 (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

TODO 38: Pandigital multiples PI

Take the number 192 and multiply it by each of 1, 2, and 3:

192 × 1 = 192 192 × 2 = 384 192 × 3 = 576 By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)

The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).

What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n > 1?

TODO 46: Goldbach's other conjecture PI

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 2×12 15 = 7 + 2×22 21 = 3 + 2×32 25 = 7 + 2×32 27 = 19 + 2×22 33 = 31 + 2×12

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

DONE 48: Self powers

The series, 1^1 + 2^2 + 3^3 + ... + 10^10 = 10405071317.

Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000.

A

This is not super fast, but its bearable, result 9110846700 It's fun to watch the number grow as well :)

1(defun pe-selfpower (max)
2  (let ( (sum 0))
3    (cl-loop for i from 1 to max do
4	     (setq sum (calcFunc-add sum (calcFunc-pow i i)))
5	     ) sum)
6  )
7
8(math-format-number (pe-selfpower 1000))

TODO 49: Prime permutations US

The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?

TODO 55: Lychrel numbers FF

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292, 1292 + 2921 = 4213 4213 + 3124 = 7337

That is, 349 took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.

How many Lychrel numbers are there below ten-thousand?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.

TODO 64: Odd period square roots US

Problem 64 All square roots are periodic when written as continued fractions and can be written in the form:

√N = a0 + 1 a1 + 1 a2 + 1 a3 + ... For example, let us consider √23:

√23 = 4 + √23 — 4 = 4 + 1 = 4 + 1

1 √23—4 1 + √23 – 3 7 If we continue we would get the following expansion:

√23 = 4 + 1 1 + 1 3 + 1 1 + 1 8 + ... The process can be summarised as follows:

a0 = 4, 1 √23—4

√23+4 7 = 1 + √23—3 7 a1 = 1, 7 √23—3

7(√23+3) 14 = 3 + √23—3 2 a2 = 3, 2 √23—3

2(√23+3) 14 = 1 + √23—4 7 a3 = 1, 7 √23—4

7(√23+4) 7 = 8 + √23—4 a4 = 8, 1 √23—4

√23+4 7 = 1 + √23—3 7 a5 = 1, 7 √23—3

7(√23+3) 14 = 3 + √23—3 2 a6 = 3, 2 √23—3

2(√23+3) 14 = 1 + √23—4 7 a7 = 1, 7 √23—4

7(√23+4) 7 = 8 + √23—4 It can be seen that the sequence is repeating. For conciseness, we use the notation √23 = [4;(1,3,1,8)], to indicate that the block (1,3,1,8) repeats indefinitely.

The first ten continued fraction representations of (irrational) square roots are:

√2=[1;(2)], period=1 √3=[1;(1,2)], period=2 √5=[2;(4)], period=1 √6=[2;(2,4)], period=2 √7=[2;(1,1,1,4)], period=4 √8=[2;(1,4)], period=2 √10=[3;(6)], period=1 √11=[3;(3,6)], period=2 √12= [3;(2,6)], period=2 √13=[3;(1,1,1,1,6)], period=5

Exactly four continued fractions, for N ≤ 13, have an odd period.

How many continued fractions for N ≤ 10000 have an odd period?

TODO 65: Convergents of e PI

The square root of 2 can be written as an infinite continued fraction.

√2 = 1 + 1

2 +

1

 	2 +

1

 	 	2 +

1

 	 	 	2 + ...

The infinite continued fraction can be written, √2 = [1;(2)], (2) indicates that 2 repeats ad infinitum. In a similar way, √23 = [4;(1,3,1,8)].

It turns out that the sequence of partial values of continued fractions for square roots provide the best rational approximations. Let us consider the convergents for √2.

1 + 1

= 3/2

2

1 + 1

= 7/5 2 + 1

2

1 + 1

= 17/12 2 + 1

 	2 +

1

2

1 + 1

= 41/29 2 + 1

 	2 +

1

 	 	2 +

1

2

Hence the sequence of the first ten convergents for √2 are:

1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, ... What is most surprising is that the important mathematical constant, e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...].

The first ten terms in the sequence of convergents for e are:

2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ... The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17.

Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.

DONE 67: Maximum path sum II

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3 7 4 2 4 6 8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)

A

This was pretty simple because i just reused pe-18!

  1
  2    (setq pe-67-pyramid
  3  [
  4  [  59]
  5  [  73 41]
  6  [  52 40 09]
  7  [  26 53 06 34]
  8  [  10 51 87 86 81]
  9  [  61 95 66 57 25 68]
 10  [  90 81 80 38 92 67 73]
 11  [  30 28 51 76 81 18 75 44]
 12  [  84 14 95 87 62 81 17 78 58]
 13  [  21 46 71 58 02 79 62 39 31 09]
 14  [  56 34 35 53 78 31 81 18 90 93 15]
 15  [  78 53 04 21 84 93 32 13 97 11 37 51]
 16  [  45 03 81 79 05 18 78 86 13 30 63 99 95]
 17  [  39 87 96 28 03 38 42 17 82 87 58 07 22 57]
 18  [  06 17 51 17 07 93 09 07 75 97 95 78 87 08 53]
 19  [  67 66 59 60 88 99 94 65 55 77 55 34 27 53 78 28]
 20  [  76 40 41 04 87 16 09 42 75 69 23 97 30 60 10 79 87]
 21  [  12 10 44 26 21 36 32 84 98 60 13 12 36 16 63 31 91 35]
 22  [  70 39 06 05 55 27 38 48 28 22 34 35 62 62 15 14 94 89 86]
 23  [  66 56 68 84 96 21 34 34 34 81 62 40 65 54 62 05 98 03 02 60]
 24  [  38 89 46 37 99 54 34 53 36 14 70 26 02 90 45 13 31 61 83 73 47]
 25  [  36 10 63 96 60 49 41 05 37 42 14 58 84 93 96 17 09 43 05 43 06 59]
 26  [  66 57 87 57 61 28 37 51 84 73 79 15 39 95 88 87 43 39 11 86 77 74 18]
 27  [  54 42 05 79 30 49 99 73 46 37 50 02 45 09 54 52 27 95 27 65 19 45 26 45]
 28  [  71 39 17 78 76 29 52 90 18 99 78 19 35 62 71 19 23 65 93 85 49 33 75 09 02]
 29  [  33 24 47 61 60 55 32 88 57 55 91 54 46 57 07 77 98 52 80 99 24 25 46 78 79 05]
 30  [  92 09 13 55 10 67 26 78 76 82 63 49 51 31 24 68 05 57 07 54 69 21 67 43 17 63 12]
 31  [  24 59 06 08 98 74 66 26 61 60 13 03 09 09 24 30 71 08 88 70 72 70 29 90 11 82 41 34]
 32  [  66 82 67 04 36 60 92 77 91 85 62 49 59 61 30 90 29 94 26 41 89 04 53 22 83 41 09 74 90]
 33  [  48 28 26 37 28 52 77 26 51 32 18 98 79 36 62 13 17 08 19 54 89 29 73 68 42 14 08 16 70 37]
 34  [  37 60 69 70 72 71 09 59 13 60 38 13 57 36 09 30 43 89 30 39 15 02 44 73 05 73 26 63 56 86 12]
 35  [  55 55 85 50 62 99 84 77 28 85 03 21 27 22 19 26 82 69 54 04 13 07 85 14 01 15 70 59 89 95 10 19]
 36  [  04 09 31 92 91 38 92 86 98 75 21 05 64 42 62 84 36 20 73 42 21 23 22 51 51 79 25 45 85 53 03 43 22]
 37  [  75 63 02 49 14 12 89 14 60 78 92 16 44 82 38 30 72 11 46 52 90 27 08 65 78 03 85 41 57 79 39 52 33 48]
 38  [  78 27 56 56 39 13 19 43 86 72 58 95 39 07 04 34 21 98 39 15 39 84 89 69 84 46 37 57 59 35 59 50 26 15 93]
 39  [  42 89 36 27 78 91 24 11 17 41 05 94 07 69 51 96 03 96 47 90 90 45 91 20 50 56 10 32 36 49 04 53 85 92 25 65]
 40  [  52 09 61 30 61 97 66 21 96 92 98 90 06 34 96 60 32 69 68 33 75 84 18 31 71 50 84 63 03 03 19 11 28 42 75 45 45]
 41  [  61 31 61 68 96 34 49 39 05 71 76 59 62 67 06 47 96 99 34 21 32 47 52 07 71 60 42 72 94 56 82 83 84 40 94 87 82 46]
 42  [  01 20 60 14 17 38 26 78 66 81 45 95 18 51 98 81 48 16 53 88 37 52 69 95 72 93 22 34 98 20 54 27 73 61 56 63 60 34 63]
 43  [  93 42 94 83 47 61 27 51 79 79 45 01 44 73 31 70 83 42 88 25 53 51 30 15 65 94 80 44 61 84 12 77 02 62 02 65 94 42 14 94]
 44  [  32 73 09 67 68 29 74 98 10 19 85 48 38 31 85 67 53 93 93 77 47 67 39 72 94 53 18 43 77 40 78 32 29 59 24 06 02 83 50 60 66]
 45  [  32 01 44 30 16 51 15 81 98 15 10 62 86 79 50 62 45 60 70 38 31 85 65 61 64 06 69 84 14 22 56 43 09 48 66 69 83 91 60 40 36 61]
 46  [  92 48 22 99 15 95 64 43 01 16 94 02 99 19 17 69 11 58 97 56 89 31 77 45 67 96 12 73 08 20 36 47 81 44 50 64 68 85 40 81 85 52 09]
 47  [  91 35 92 45 32 84 62 15 19 64 21 66 06 01 52 80 62 59 12 25 88 28 91 50 40 16 22 99 92 79 87 51 21 77 74 77 07 42 38 42 74 83 02 05]
 48  [  46 19 77 66 24 18 05 32 02 84 31 99 92 58 96 72 91 36 62 99 55 29 53 42 12 37 26 58 89 50 66 19 82 75 12 48 24 87 91 85 02 07 03 76 86]
 49  [  99 98 84 93 07 17 33 61 92 20 66 60 24 66 40 30 67 05 37 29 24 96 03 27 70 62 13 04 45 47 59 88 43 20 66 15 46 92 30 04 71 66 78 70 53 99]
 50  [  67 60 38 06 88 04 17 72 10 99 71 07 42 25 54 05 26 64 91 50 45 71 06 30 67 48 69 82 08 56 80 67 18 46 66 63 01 20 08 80 47 07 91 16 03 79 87]
 51  [  18 54 78 49 80 48 77 40 68 23 60 88 58 80 33 57 11 69 55 53 64 02 94 49 60 92 16 35 81 21 82 96 25 24 96 18 02 05 49 03 50 77 06 32 84 27 18 38]
 52  [  68 01 50 04 03 21 42 94 53 24 89 05 92 26 52 36 68 11 85 01 04 42 02 45 15 06 50 04 53 73 25 74 81 88 98 21 67 84 79 97 99 20 95 04 40 46 02 58 87]
 53  [  94 10 02 78 88 52 21 03 88 60 06 53 49 71 20 91 12 65 07 49 21 22 11 41 58 99 36 16 09 48 17 24 52 36 23 15 72 16 84 56 02 99 43 76 81 71 29 39 49 17]
 54  [  64 39 59 84 86 16 17 66 03 09 43 06 64 18 63 29 68 06 23 07 87 14 26 35 17 12 98 41 53 64 78 18 98 27 28 84 80 67 75 62 10 11 76 90 54 10 05 54 41 39 66]
 55  [  43 83 18 37 32 31 52 29 95 47 08 76 35 11 04 53 35 43 34 10 52 57 12 36 20 39 40 55 78 44 07 31 38 26 08 15 56 88 86 01 52 62 10 24 32 05 60 65 53 28 57 99]
 56  [  03 50 03 52 07 73 49 92 66 80 01 46 08 67 25 36 73 93 07 42 25 53 13 96 76 83 87 90 54 89 78 22 78 91 73 51 69 09 79 94 83 53 09 40 69 62 10 79 49 47 03 81 30]
 57  [  71 54 73 33 51 76 59 54 79 37 56 45 84 17 62 21 98 69 41 95 65 24 39 37 62 03 24 48 54 64 46 82 71 78 33 67 09 16 96 68 52 74 79 68 32 21 13 78 96 60 09 69 20 36]
 58  [  73 26 21 44 46 38 17 83 65 98 07 23 52 46 61 97 33 13 60 31 70 15 36 77 31 58 56 93 75 68 21 36 69 53 90 75 25 82 39 50 65 94 29 30 11 33 11 13 96 02 56 47 07 49 02]
 59  [  76 46 73 30 10 20 60 70 14 56 34 26 37 39 48 24 55 76 84 91 39 86 95 61 50 14 53 93 64 67 37 31 10 84 42 70 48 20 10 72 60 61 84 79 69 65 99 73 89 25 85 48 92 56 97 16]
 60  [  03 14 80 27 22 30 44 27 67 75 79 32 51 54 81 29 65 14 19 04 13 82 04 91 43 40 12 52 29 99 07 76 60 25 01 07 61 71 37 92 40 47 99 66 57 01 43 44 22 40 53 53 09 69 26 81 07]
 61  [  49 80 56 90 93 87 47 13 75 28 87 23 72 79 32 18 27 20 28 10 37 59 21 18 70 04 79 96 03 31 45 71 81 06 14 18 17 05 31 50 92 79 23 47 09 39 47 91 43 54 69 47 42 95 62 46 32 85]
 62  [  37 18 62 85 87 28 64 05 77 51 47 26 30 65 05 70 65 75 59 80 42 52 25 20 44 10 92 17 71 95 52 14 77 13 24 55 11 65 26 91 01 30 63 15 49 48 41 17 67 47 03 68 20 90 98 32 04 40 68]
 63  [  90 51 58 60 06 55 23 68 05 19 76 94 82 36 96 43 38 90 87 28 33 83 05 17 70 83 96 93 06 04 78 47 80 06 23 84 75 23 87 72 99 14 50 98 92 38 90 64 61 58 76 94 36 66 87 80 51 35 61 38]
 64  [  57 95 64 06 53 36 82 51 40 33 47 14 07 98 78 65 39 58 53 06 50 53 04 69 40 68 36 69 75 78 75 60 03 32 39 24 74 47 26 90 13 40 44 71 90 76 51 24 36 50 25 45 70 80 61 80 61 43 90 64 11]
 65  [  18 29 86 56 68 42 79 10 42 44 30 12 96 18 23 18 52 59 02 99 67 46 60 86 43 38 55 17 44 93 42 21 55 14 47 34 55 16 49 24 23 29 96 51 55 10 46 53 27 92 27 46 63 57 30 65 43 27 21 20 24 83]
 66  [  81 72 93 19 69 52 48 01 13 83 92 69 20 48 69 59 20 62 05 42 28 89 90 99 32 72 84 17 08 87 36 03 60 31 36 36 81 26 97 36 48 54 56 56 27 16 91 08 23 11 87 99 33 47 02 14 44 73 70 99 43 35 33]
 67  [  90 56 61 86 56 12 70 59 63 32 01 15 81 47 71 76 95 32 65 80 54 70 34 51 40 45 33 04 64 55 78 68 88 47 31 47 68 87 03 84 23 44 89 72 35 08 31 76 63 26 90 85 96 67 65 91 19 14 17 86 04 71 32 95]
 68  [  37 13 04 22 64 37 37 28 56 62 86 33 07 37 10 44 52 82 52 06 19 52 57 75 90 26 91 24 06 21 14 67 76 30 46 14 35 89 89 41 03 64 56 97 87 63 22 34 03 79 17 45 11 53 25 56 96 61 23 18 63 31 37 37 47]
 69  [  77 23 26 70 72 76 77 04 28 64 71 69 14 85 96 54 95 48 06 62 99 83 86 77 97 75 71 66 30 19 57 90 33 01 60 61 14 12 90 99 32 77 56 41 18 14 87 49 10 14 90 64 18 50 21 74 14 16 88 05 45 73 82 47 74 44]
 70  [  22 97 41 13 34 31 54 61 56 94 03 24 59 27 98 77 04 09 37 40 12 26 87 09 71 70 07 18 64 57 80 21 12 71 83 94 60 39 73 79 73 19 97 32 64 29 41 07 48 84 85 67 12 74 95 20 24 52 41 67 56 61 29 93 35 72 69]
 71  [  72 23 63 66 01 11 07 30 52 56 95 16 65 26 83 90 50 74 60 18 16 48 43 77 37 11 99 98 30 94 91 26 62 73 45 12 87 73 47 27 01 88 66 99 21 41 95 80 02 53 23 32 61 48 32 43 43 83 14 66 95 91 19 81 80 67 25 88]
 72  [  08 62 32 18 92 14 83 71 37 96 11 83 39 99 05 16 23 27 10 67 02 25 44 11 55 31 46 64 41 56 44 74 26 81 51 31 45 85 87 09 81 95 22 28 76 69 46 48 64 87 67 76 27 89 31 11 74 16 62 03 60 94 42 47 09 34 94 93 72]
 73  [  56 18 90 18 42 17 42 32 14 86 06 53 33 95 99 35 29 15 44 20 49 59 25 54 34 59 84 21 23 54 35 90 78 16 93 13 37 88 54 19 86 67 68 55 66 84 65 42 98 37 87 56 33 28 58 38 28 38 66 27 52 21 81 15 08 22 97 32 85 27]
 74  [  91 53 40 28 13 34 91 25 01 63 50 37 22 49 71 58 32 28 30 18 68 94 23 83 63 62 94 76 80 41 90 22 82 52 29 12 18 56 10 08 35 14 37 57 23 65 67 40 72 39 93 39 70 89 40 34 07 46 94 22 20 05 53 64 56 30 05 56 61 88 27]
 75  [  23 95 11 12 37 69 68 24 66 10 87 70 43 50 75 07 62 41 83 58 95 93 89 79 45 39 02 22 05 22 95 43 62 11 68 29 17 40 26 44 25 71 87 16 70 85 19 25 59 94 90 41 41 80 61 70 55 60 84 33 95 76 42 63 15 09 03 40 38 12 03 32]
 76  [  09 84 56 80 61 55 85 97 16 94 82 94 98 57 84 30 84 48 93 90 71 05 95 90 73 17 30 98 40 64 65 89 07 79 09 19 56 36 42 30 23 69 73 72 07 05 27 61 24 31 43 48 71 84 21 28 26 65 65 59 65 74 77 20 10 81 61 84 95 08 52 23 70]
 77  [  47 81 28 09 98 51 67 64 35 51 59 36 92 82 77 65 80 24 72 53 22 07 27 10 21 28 30 22 48 82 80 48 56 20 14 43 18 25 50 95 90 31 77 08 09 48 44 80 90 22 93 45 82 17 13 96 25 26 08 73 34 99 06 49 24 06 83 51 40 14 15 10 25 01]
 78  [  54 25 10 81 30 64 24 74 75 80 36 75 82 60 22 69 72 91 45 67 03 62 79 54 89 74 44 83 64 96 66 73 44 30 74 50 37 05 09 97 70 01 60 46 37 91 39 75 75 18 58 52 72 78 51 81 86 52 08 97 01 46 43 66 98 62 81 18 70 93 73 08 32 46 34]
 79  [  96 80 82 07 59 71 92 53 19 20 88 66 03 26 26 10 24 27 50 82 94 73 63 08 51 33 22 45 19 13 58 33 90 15 22 50 36 13 55 06 35 47 82 52 33 61 36 27 28 46 98 14 73 20 73 32 16 26 80 53 47 66 76 38 94 45 02 01 22 52 47 96 64 58 52 39]
 80  [  88 46 23 39 74 63 81 64 20 90 33 33 76 55 58 26 10 46 42 26 74 74 12 83 32 43 09 02 73 55 86 54 85 34 28 23 29 79 91 62 47 41 82 87 99 22 48 90 20 05 96 75 95 04 43 28 81 39 81 01 28 42 78 25 39 77 90 57 58 98 17 36 73 22 63 74 51]
 81  [  29 39 74 94 95 78 64 24 38 86 63 87 93 06 70 92 22 16 80 64 29 52 20 27 23 50 14 13 87 15 72 96 81 22 08 49 72 30 70 24 79 31 16 64 59 21 89 34 96 91 48 76 43 53 88 01 57 80 23 81 90 79 58 01 80 87 17 99 86 90 72 63 32 69 14 28 88 69]
 82  [  37 17 71 95 56 93 71 35 43 45 04 98 92 94 84 96 11 30 31 27 31 60 92 03 48 05 98 91 86 94 35 90 90 08 48 19 33 28 68 37 59 26 65 96 50 68 22 07 09 49 34 31 77 49 43 06 75 17 81 87 61 79 52 26 27 72 29 50 07 98 86 01 17 10 46 64 24 18 56]
 83  [  51 30 25 94 88 85 79 91 40 33 63 84 49 67 98 92 15 26 75 19 82 05 18 78 65 93 61 48 91 43 59 41 70 51 22 15 92 81 67 91 46 98 11 11 65 31 66 10 98 65 83 21 05 56 05 98 73 67 46 74 69 34 08 30 05 52 07 98 32 95 30 94 65 50 24 63 28 81 99 57]
 84  [  19 23 61 36 09 89 71 98 65 17 30 29 89 26 79 74 94 11 44 48 97 54 81 55 39 66 69 45 28 47 13 86 15 76 74 70 84 32 36 33 79 20 78 14 41 47 89 28 81 05 99 66 81 86 38 26 06 25 13 60 54 55 23 53 27 05 89 25 23 11 13 54 59 54 56 34 16 24 53 44 06]
 85  [  13 40 57 72 21 15 60 08 04 19 11 98 34 45 09 97 86 71 03 15 56 19 15 44 97 31 90 04 87 87 76 08 12 30 24 62 84 28 12 85 82 53 99 52 13 94 06 65 97 86 09 50 94 68 69 74 30 67 87 94 63 07 78 27 80 36 69 41 06 92 32 78 37 82 30 05 18 87 99 72 19 99]
 86  [  44 20 55 77 69 91 27 31 28 81 80 27 02 07 97 23 95 98 12 25 75 29 47 71 07 47 78 39 41 59 27 76 13 15 66 61 68 35 69 86 16 53 67 63 99 85 41 56 08 28 33 40 94 76 90 85 31 70 24 65 84 65 99 82 19 25 54 37 21 46 33 02 52 99 51 33 26 04 87 02 08 18 96]
 87  [  54 42 61 45 91 06 64 79 80 82 32 16 83 63 42 49 19 78 65 97 40 42 14 61 49 34 04 18 25 98 59 30 82 72 26 88 54 36 21 75 03 88 99 53 46 51 55 78 22 94 34 40 68 87 84 25 30 76 25 08 92 84 42 61 40 38 09 99 40 23 29 39 46 55 10 90 35 84 56 70 63 23 91 39]
 88  [  52 92 03 71 89 07 09 37 68 66 58 20 44 92 51 56 13 71 79 99 26 37 02 06 16 67 36 52 58 16 79 73 56 60 59 27 44 77 94 82 20 50 98 33 09 87 94 37 40 83 64 83 58 85 17 76 53 02 83 52 22 27 39 20 48 92 45 21 09 42 24 23 12 37 52 28 50 78 79 20 86 62 73 20 59]
 89  [  54 96 80 15 91 90 99 70 10 09 58 90 93 50 81 99 54 38 36 10 30 11 35 84 16 45 82 18 11 97 36 43 96 79 97 65 40 48 23 19 17 31 64 52 65 65 37 32 65 76 99 79 34 65 79 27 55 33 03 01 33 27 61 28 66 08 04 70 49 46 48 83 01 45 19 96 13 81 14 21 31 79 93 85 50 05]
 90  [  92 92 48 84 59 98 31 53 23 27 15 22 79 95 24 76 05 79 16 93 97 89 38 89 42 83 02 88 94 95 82 21 01 97 48 39 31 78 09 65 50 56 97 61 01 07 65 27 21 23 14 15 80 97 44 78 49 35 33 45 81 74 34 05 31 57 09 38 94 07 69 54 69 32 65 68 46 68 78 90 24 28 49 51 45 86 35]
 91  [  41 63 89 76 87 31 86 09 46 14 87 82 22 29 47 16 13 10 70 72 82 95 48 64 58 43 13 75 42 69 21 12 67 13 64 85 58 23 98 09 37 76 05 22 31 12 66 50 29 99 86 72 45 25 10 28 19 06 90 43 29 31 67 79 46 25 74 14 97 35 76 37 65 46 23 82 06 22 30 76 93 66 94 17 96 13 20 72]
 92  [  63 40 78 08 52 09 90 41 70 28 36 14 46 44 85 96 24 52 58 15 87 37 05 98 99 39 13 61 76 38 44 99 83 74 90 22 53 80 56 98 30 51 63 39 44 30 91 91 04 22 27 73 17 35 53 18 35 45 54 56 27 78 48 13 69 36 44 38 71 25 30 56 15 22 73 43 32 69 59 25 93 83 45 11 34 94 44 39 92]
 93  [  12 36 56 88 13 96 16 12 55 54 11 47 19 78 17 17 68 81 77 51 42 55 99 85 66 27 81 79 93 42 65 61 69 74 14 01 18 56 12 01 58 37 91 22 42 66 83 25 19 04 96 41 25 45 18 69 96 88 36 93 10 12 98 32 44 83 83 04 72 91 04 27 73 07 34 37 71 60 59 31 01 54 54 44 96 93 83 36 04 45]
 94  [  30 18 22 20 42 96 65 79 17 41 55 69 94 81 29 80 91 31 85 25 47 26 43 49 02 99 34 67 99 76 16 14 15 93 08 32 99 44 61 77 67 50 43 55 87 55 53 72 17 46 62 25 50 99 73 05 93 48 17 31 70 80 59 09 44 59 45 13 74 66 58 94 87 73 16 14 85 38 74 99 64 23 79 28 71 42 20 37 82 31 23]
 95  [  51 96 39 65 46 71 56 13 29 68 53 86 45 33 51 49 12 91 21 21 76 85 02 17 98 15 46 12 60 21 88 30 92 83 44 59 42 50 27 88 46 86 94 73 45 54 23 24 14 10 94 21 20 34 23 51 04 83 99 75 90 63 60 16 22 33 83 70 11 32 10 50 29 30 83 46 11 05 31 17 86 42 49 01 44 63 28 60 07 78 95 40]
 96  [  44 61 89 59 04 49 51 27 69 71 46 76 44 04 09 34 56 39 15 06 94 91 75 90 65 27 56 23 74 06 23 33 36 69 14 39 05 34 35 57 33 22 76 46 56 10 61 65 98 09 16 69 04 62 65 18 99 76 49 18 72 66 73 83 82 40 76 31 89 91 27 88 17 35 41 35 32 51 32 67 52 68 74 85 80 57 07 11 62 66 47 22 67]
 97  [  65 37 19 97 26 17 16 24 24 17 50 37 64 82 24 36 32 11 68 34 69 31 32 89 79 93 96 68 49 90 14 23 04 04 67 99 81 74 70 74 36 96 68 09 64 39 88 35 54 89 96 58 66 27 88 97 32 14 06 35 78 20 71 06 85 66 57 02 58 91 72 05 29 56 73 48 86 52 09 93 22 57 79 42 12 01 31 68 17 59 63 76 07 77]
 98  [  73 81 14 13 17 20 11 09 01 83 08 85 91 70 84 63 62 77 37 07 47 01 59 95 39 69 39 21 99 09 87 02 97 16 92 36 74 71 90 66 33 73 73 75 52 91 11 12 26 53 05 26 26 48 61 50 90 65 01 87 42 47 74 35 22 73 24 26 56 70 52 05 48 41 31 18 83 27 21 39 80 85 26 08 44 02 71 07 63 22 05 52 19 08 20]
 99  [  17 25 21 11 72 93 33 49 64 23 53 82 03 13 91 65 85 02 40 05 42 31 77 42 05 36 06 54 04 58 07 76 87 83 25 57 66 12 74 33 85 37 74 32 20 69 03 97 91 68 82 44 19 14 89 28 85 85 80 53 34 87 58 98 88 78 48 65 98 40 11 57 10 67 70 81 60 79 74 72 97 59 79 47 30 20 54 80 89 91 14 05 33 36 79 39]
100  [  60 85 59 39 60 07 57 76 77 92 06 35 15 72 23 41 45 52 95 18 64 79 86 53 56 31 69 11 91 31 84 50 44 82 22 81 41 40 30 42 30 91 48 94 74 76 64 58 74 25 96 57 14 19 03 99 28 83 15 75 99 01 89 85 79 50 03 95 32 67 44 08 07 41 62 64 29 20 14 76 26 55 48 71 69 66 19 72 44 25 14 01 48 74 12 98 07]
101  [  64 66 84 24 18 16 27 48 20 14 47 69 30 86 48 40 23 16 61 21 51 50 26 47 35 33 91 28 78 64 43 68 04 79 51 08 19 60 52 95 06 68 46 86 35 97 27 58 04 65 30 58 99 12 12 75 91 39 50 31 42 64 70 04 46 07 98 73 98 93 37 89 77 91 64 71 64 65 66 21 78 62 81 74 42 20 83 70 73 95 78 45 92 27 34 53 71 15]
102  [  30 11 85 31 34 71 13 48 05 14 44 03 19 67 23 73 19 57 06 90 94 72 57 69 81 62 59 68 88 57 55 69 49 13 07 87 97 80 89 05 71 05 05 26 38 40 16 62 45 99 18 38 98 24 21 26 62 74 69 04 85 57 77 35 58 67 91 79 79 57 86 28 66 34 72 51 76 78 36 95 63 90 08 78 47 63 45 31 22 70 52 48 79 94 15 77 61 67 68]
103  [  23 33 44 81 80 92 93 75 94 88 23 61 39 76 22 03 28 94 32 06 49 65 41 34 18 23 08 47 62 60 03 63 33 13 80 52 31 54 73 43 70 26 16 69 57 87 83 31 03 93 70 81 47 95 77 44 29 68 39 51 56 59 63 07 25 70 07 77 43 53