codeforces 743 C. Vladik and fractions (数学)

C. Vladik and fractions

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Vladik 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 109.

If there is no such answer, print -1.

Input

The single line contains single integer n (1 ≤ n ≤ 104).

Output

If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, 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

想到了 就是水题，想不到那就没法了。

数学知识：2/n = 1/n + 1/n = 1/n + 1/(n+1) + 1/[n*(n+1)]

code :

#include <iostream>#include<cstdio>using namespace std;int main(){    int n;    scanf("%d",&n);    if(n==1)        printf("-1\n");    else        printf("%d %d %d\n",n,n+1,n*(n+1));    return 0;}