Codeforces 743C-Vladik and fractions（构造）

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：给你一个n，找出一组数x，y，z，满足x！=y，y！=z，z！=z，并且2/n=1/x+1/y+1/z

解题思路：构造，因为x，y，z互不相同，可以设x=n，y=n+1，则z=n*（n+1），很明显n=1的时候是不满足的，则n=1的时候输出-1

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
#include <map>

using namespace std;

int main()
{
int n;
while(~scanf("%d",&n))
{
if(n==1) printf("-1\n");
else printf("%d %d %d\n",n,n+1,n*(n+1));
}
return 0;
}