Harmonious Matrices

2. Harmonious Matrices Call an m × n matrix of bits "harmonious" if every cell in it has an even number of 1 bits as neighbors. A cell is a neighbor of itself, and also to the cells above, below, left, and right (if they exist). So the number of neighbors of a cell is at most five, but could be less, depending on where it is. The following is an harmonious 4 × 4 square of bits: 0 1 0 0 1 1 1 0