Minimal Square

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Given two identical $a\times b$ rectangles with positive integer sides, find the smallest square area containing both. The rectangles may be rotated by 90 degrees, may touch, but cannot overlap; all edges remain axis-aligned.

Input

One line contains positive integers $a,b$.

Output

Print one integer: the minimum square area.

Subtasks

• Subtask 1 (20 points): 1 <= a,b <= 10.

• Subtask 2 (30 points): 1 <= a,b <= 50.

• Subtask 3 (50 points): 1 <= a,b <= 100.

Examples

Example 1

Input

3 2

Output

16

Explanation

For this input, the case-specific computation and the required exact output are shown above. The required square side is 4, giving area 16.

Example 2

Input

4 7

Output

64

Explanation

For this input, the case-specific computation and the required exact output are shown above. The square side is 8, giving area 64.