Codeforces Round #368 (Div. 2) C. Pythagorean Triples（数学构造）

Codeforces Round #368 (Div. 2) C. Pythagorean Triples（数学构造）

C. Pythagorean Triples

time limit per test

memory limit per test

input

output

Pythagorean triples.

(3, 4, 5), (5, 12, 13) and (6, 8, 10)

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

n (1 ≤ n ≤ 109) — the length of some side of a right triangle.

Output

m and k (1 ≤ m, k ≤ 1018), such that n, m and k

n, print  - 1

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：给你直角三角形的一边，让你求出其余的两边，要求是整数。

题解：数学构造题啊。直角三角形：k为奇：（2k+1，2k^2+2k,2k^2+2k+1）。 k为偶：（2k，k^2-1,k^2+1）

代码：

#pragma comment(linker, "/STACK:102400000,102400000")//#include#include#include#include#include#include#include#include

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