codeforces 707C Pythagorean Triples（數學）

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

題意：給你一條邊的長度，問你能否找到兩條邊使他們能夠組成直角三角形

思路：在這裡我們可以假設他給出的邊為一條直角邊，則其他邊可由數學公式可得，具體見代碼。。

#include<cstdio>
int main()
{
    __int64 n;
    while(~scanf("%I64d",&n))
    {
        if(n == 1 || n == 2)
            printf("-1\n");
        else if(n * n % 2)
            printf("%I64d %I64d\n",(n * n - 1) / 2 , (n * n + 1) / 2);
        else
            printf("%I64d %I64d\n",(n * n / 2 - 2) / 2 , (n * n / 2 + 2) / 2);
    }
    return 0;
}