Codeforces Round 384 (Div. 2) |
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Finished |

brute force

constructive algorithms

math

number theory

*1500

No tag edit access

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C. Vladik and fractions

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer *n* he can represent fraction as a sum of three distinct positive fractions in form .

Help Vladik with that, i.e for a given *n* find three distinct positive integers *x*, *y* and *z* such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 10^{9}.

If there is no such answer, print -1.

Input

The single line contains single integer *n* (1 ≤ *n* ≤ 10^{4}).

Output

If the answer exists, print 3 distinct numbers *x*, *y* and *z* (1 ≤ *x*, *y*, *z* ≤ 10^{9}, *x* ≠ *y*, *x* ≠ *z*, *y* ≠ *z*). Otherwise print -1.

If there are multiple answers, print any of them.

Examples

Input

3

Output

2 7 42

Input

7

Output

7 8 56

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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