public static int countConnections(List<List<Integer>> matrix) {
        int m = matrix.size();
        if (m == 0) return 0;
        int n = matrix.get(0).size();

        // Only these 4 directions to avoid double-counting:
        int[][] directions = {
            {0, 1},   // right
            {1, 0},   // down
            {1, 1},   // down-right
            {1, -1}   // down-left
        };

        int count = 0;

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (matrix.get(i).get(j) == 1) {
                    for (int[] dir : directions) {
                        int ni = i + dir[0];
                        int nj = j + dir[1];

                        if (ni >= 0 && ni < m && nj >= 0 && nj < n && matrix.get(ni).get(nj) == 1) {
                            count++;
                        }
                    }
                }
            }
        }

        return count;
    }