Count Submatrices

Problem

Given a 2D matrix mat which may contain both positive and negative integers, return the total number of non-empty submatrices that sum to zero.

Examples

countZeroSumSubmatrices([
  [0, 2, -3],
  [1, -3, 1],
  [1, -2, 1]
]) 
// returns 3
/* 
The function identifies the following
submatrices with a sum of zero:
1. A 1x1 zone at the position [0,0]: [[0]]
2. A 2x2 zone at the position [0,0]: [[0,2],[1,-3]]
3. A 1x3 zone at the position [0,2]: [[1,-2,1]]
*/