Codeforces Round #384 (Div. 2)（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

题解：2/n=1/n+1/n，那我们让其中一个是n，原问题就变成了1/n=1/x+1/y,通分变形一下(x-n)(y-n)=n*n,那我们让x-n=1,y-n=n*n即可，由于x,y,z要不同，所以当n是1的时候是不行的。

#include <bits/stdc++.h>#define ll long longusing namespace std;int main(){    ll n;  cin>>n;        if(n==1)        {            printf("-1\n");        }        else        printf("%I64d %I64d %I64d\n",n,n+1,n*(n+1));}