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Tiling a Rectangle with the Fewest Squares

Given a rectangle of size n x m, return the minimum number of integer-sided squares that tile the rectangle.

Given a rectangle of size n x m, return the minimum number of integer-sided squares that tile the rectangle.

Example 1

Input: n = 2, m = 3

Output: 3

Explanation: 3 squares are necessary to cover the rectangle. 2 (squares of 1x1) 1 (square of 2x2)

Example 2

Input: n = 5, m = 8

Output: 5

Example 3

Input: n = 11, m = 13

Output: 6

Constraints

  • 1 <= n, m <= 13

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