Increment Submatrices by One

Medium

You receive a positive integer n, indicating that we initially have an n x n 0-indexed integer matrix mat filled with zeroes.

You are also given a 2D integer array query. For each query[i] = [row1 i, col1 i, row2 i, col2 i ], you should do the following operation:

Add 1 to every element in the submatrix with the top left corner (row1 i, col1 i ) and the bottom right corner (row2 i, col2 i ). That is, add 1 to mat[x][y] for all row1 i <= x <= row2 i and col1 i <= y <= col2 i.

Produce the matrix mat after performing every query.

Example 1

Original illustrative diagram 1 for Increment Submatrices by One

Input: n = 3, queries = [[1,1,2,2],[0,0,1,1]]

Output: [[1,1,0],[1,2,1],[0,1,1]]

Explanation: The diagram above shows the initial matrix, the matrix after the first query, and the matrix after the second query.

In the first query, we add 1 to every element in the submatrix with the top left corner (1, 1) and bottom right corner (2, 2).
In the second query, we add 1 to every element in the submatrix with the top left corner (0, 0) and bottom right corner (1, 1).

Example 2

Original illustrative diagram 2 for Increment Submatrices by One

Input: n = 2, queries = [[0,0,1,1]]

Output: [[1,1],[1,1]]

Explanation: The diagram above shows the initial matrix and the matrix after the first query.

Constraints

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