You are given an $m × n$ matrix of integers. Your task is to determine the length of the longest strictly increasing path within the matrix.

A path is defined by consecutively moving from one cell to another adjacent cell. From any cell, movement is allowed only in four directions: up, down, left and right.

Diagonal movement is not allowed. You also cannot move outside the matrix boundaries (no wrap-around).

A path is considered increasing if each subsequent cell contains a strictly greater integer than the previous one.

Your goal is to return the maximum length among all possible increasing paths in the matrix.

Constraints:

• $m ==$ matrix.length

• $n ==$ matrix[i].length

• $1 <= m, n <= 200$

• $0 <=$ matrix[i][j] $<= 2^{31} - 1$

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.