Square Neighborhood Sums

You are given an m x n integer matrix grid and an integer radius.

Return a matrix answer of the same shape as grid, where answer[i][j] is the sum of every grid[r][c] such that

• i - radius <= r <= i + radius,
• j - radius <= c <= j + radius, and
• (r, c) is inside the grid.

In other words, each cell sums the square of side 2 * radius + 1 centred on it. Near the border the square is clipped to the grid; it never wraps around and never reads outside.

Examples

Example 1

Input: grid = [[1,2,3],[4,5,6],[7,8,9]], radius = 1
Output: [[12,21,16],[27,45,33],[24,39,28]]
Explanation: answer[0][0] sums the four cells with row and column within 1 of (0,0), namely 1, 2, 4 and 5, giving 12. answer[1][1] is centred, so it sums all nine cells: 45.

Example 2

Input: grid = [[1,2,3],[4,5,6],[7,8,9]], radius = 2
Output: [[45,45,45],[45,45,45],[45,45,45]]
Explanation: The radius reaches every cell from every position, so each entry is the sum of the whole grid.