Cut a Rectangle Into Squares

On each move, choose one rectangle and cut all the way across it, parallel to a side, making two rectangles with positive integer side lengths. Continue until every piece is a square. Squares may have different sizes. Count cuts, not pieces.

Implement rectangle_cutting(height, width).

Input

height: The starting rectangle height.

width: The starting rectangle width.

Output

Return the minimum number of cuts.

Vincoli

1 ≤ height, width ≤ 500. Rotation does not change the answer.

Esempi

Input:
width = 3
height = 2

Output atteso:
expected = 2

Input:
long long width = 3;
long long height = 2;

Output atteso:
long long expected = 2;

Input:
long width = 3;
long height = 2;

Output atteso:
long expected = 2;

Input:
width = 4
height = 4

Output atteso:
expected = 0

Input:
long long width = 4;
long long height = 4;

Output atteso:
long long expected = 0;

Input:
long width = 4;
long height = 4;

Output atteso:
long expected = 0;

Riferimenti

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• Rectangle Cutting — 1744