Codeforces Round #384 (Div. 2) 743C Vladik and fractions

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

题意：给你个n，请你找出符合条件的x,y,z.

这题有比较巧妙的方法。

我们先令x,y,z中任意一个数为n   ,这里我们让z=n    那么这个式子可以化简成：1/n=1/x+1/y

解一下这个式子：就能解除：y=(x*n)/(x-n)

如果要让y为整数的话。可以使这个式子的分母为1

那么x=N+1

则y=n*(n+1)

当n为1的时候，x,y,z不存在，输出-1

#include<bits/stdc++.h>using namespace std;int main(){    int n;    while(~scanf("%d",&n))    {        if(n==1)        {            printf("-1\n");            continue;        }        printf("%d %d %d\n",n+1,n*(n+1),n);    }    return 0;}