codeforces 707 C Pythagorean Triples【数学】

C. Pythagorean Triples

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Katya studies in a fifth grade. Recently her class studied right triangles and the Pythagorean theorem. It appeared, that there are triples of positive integers such that you can construct a right triangle with segments of lengths corresponding to triple. Such triples are calledPythagorean triples.

For example, triples (3, 4, 5), (5, 12, 13) and (6, 8, 10) are Pythagorean triples.

Here Katya wondered if she can specify the length of some side of right triangle and find any Pythagorean triple corresponding to such length? Note that the side which length is specified can be a cathetus as well as hypotenuse.

Katya had no problems with completing this task. Will you do the same?

Input

The only line of the input contains single integer n (1 ≤ n ≤ 109) — the length of some side of a right triangle.

Output

Print two integers m and k (1 ≤ m, k ≤ 1018), such that n, m and k form a Pythagorean triple, in the only line.

In case if there is no any Pythagorean triple containing integer n, print  - 1 in the only line. If there are many answers, print any of them.

Examples

input

3

output

4 5

input

6

output

8 10

input

1

output

-1

input

17

output

144 145

input

67

output

2244 2245

Note

Illustration for the first sample.

/*
    题意：给你三角形的一条边的长度,问你是否存在有这条边的勾股数,如果存在,输出另外两个数,否则输出-1
    类型：数学
    分析：经过分析,可以发现当a>1并且a为奇数的时候,把a分解成一半 n=(a-1)/2;则b=2*n*(n+1),c=2*n*(n+1)+1;
          当a>2并且a为偶数的时候,把a分解成一半 n=a/2;则b=n*n-1,c=n*n+1;
*/
#include
#include
#include
#include
#include
#include
using namespace std;
typedef long long ll;

int main()
{
    ll a,n=-1,b,c;
    cin>>a;
    if(a%2==1&&a>1){
        n=(a-1)/2;
        b=2*n*(n+1);
        c=2*n*(n+1)+1;
    }
    else if(a%2==0&&a>2){
        n=a/2;
        b=n*n-1;
        c=n*n+1;
    }
    if(n==-1)cout<<-1<