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.

Restrições

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

Exemplos

Entrada:
width = 3
height = 2

Saída esperada:
expected = 2

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

Saída esperada:
long long expected = 2;

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

Saída esperada:
long expected = 2;

Entrada:
width = 4
height = 4

Saída esperada:
expected = 0

Entrada:
long long width = 4;
long long height = 4;

Saída esperada:
long long expected = 0;

Entrada:
long width = 4;
long height = 4;

Saída esperada:
long expected = 0;

Referências

Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.

• Rectangle Cutting — 1744