Codeforces Round #384(Div. 2)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

题目大意：

给你一个数N，让你找三个数x，y，z，使得其互不相同的情况下，满足2/n=1/x+1/y+1/z；如果没有合法情况，输出-1.

思路：

第二组样例非常666系列。

不难发现，其结果就是n，n+1，n*(n+1).

注意n==1的时候，结果为1 2 2 ，显然是不合法的情况，此时输出-1.

Ac代码：

#include<stdio.h>
#include<string.h>
using namespace std;
#define ll __int64
int main()
{
ll n;
while(~scanf("%I64d",&n))
{
if(n==1)
{
printf("-1\n");
continue;
}
else
printf("%I64d %I64d %I64d\n",n,n+1,n*(n+1));
}
}