A Prime Conjecture

Problem code: PRIMES2

All submissions for this problem are available.

Chef has been exploring prime numbers lately, and has recently made a conjecture resembling one of Goldbach's conjectures. Chef's conjecture is that any odd number greater than 61 can be expressed as the sum of a prime, a square of a prime, and a cube of a prime. He wants you to help verify his conjecture for small numbers.

Note: negative numbers are never considered to be prime, nor are 0 and 1.

Input

Input will consist of a series of odd numbers greater than 61 and less than 106, one per line, terminated by the number 0 on a line by itself. There will be at most 1000 lines.

Output

For each odd number in the input, print 3 primes P1, P2, P3 on a line, where P1 + P22 + P33 is equal to the number from the input. If no such primes exist, print "0 0 0" instead (quotes for clarity). If there are multiple triplets of primes that satisfy the equation, print any such triplet.

Sample Input

81
85
155
0

Sample Output

5 7 3
73 2 2
5 5 5
Author: pieguy
Date Added: 7-04-2011
Time Limit: 2 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

any idea to do this prob?

hellodear @ 22 Mar 2012 09:51 PM
any idea to do this prob?

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