Longest Increasing Path in a Matrix

Given an m x n integers matrix, return the length of the longest increasing path in the matrix.

From each cell, you can move in four directions: up, down, left, or right. You may not move diagonally or move outside the boundary of the matrix. You may not revisit cells within the same path.

Examples

Example 1:

Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]

Output: 4

Explanation: The longest increasing path is [1, 2, 6, 9].

Example 2:

Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]

Output: 4

Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Example 3:

Input: matrix = [[1]]

Output: 1

Explanation: The matrix has only one cell, so the longest path has length 1.

Constraints

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 200
• 0 <= matrix[i][j] <= 2^31 - 1