Same Count One

Description:

Input:

The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 2\cdot 10^4$$$)  — the number of test cases. The description of test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$2 \leq n \leq 10^5$$$, $$$2 \leq m \leq 10^5$$$).

The $$$i$$$-th of the following $$$n$$$ lines contains $$$m$$$ integers $$$a_{i, 1}, a_{i, 2}, \ldots, a_{i, m}$$$ $$$(0 \le a_{i, j} \le 1)$$$  — the elements of the $$$i$$$-th array.

It is guaranteed that the sum of $$$n \cdot m$$$ over all test cases does not exceed $$$10^6$$$.

Output:

For each test case, if the objective is not achievable, output $$$-1$$$.

Otherwise, in the first line output $$$k$$$ $$$(0 \le k \le mn)$$$  — the minimum number of operations required.

The $$$i$$$-th of the following $$$k$$$ lines should contain $$$3$$$ integers, $$$x_i, y_i, z_i$$$ $$$(1 \le x_i, y_i \le n, 1 \le z_i \le m)$$$, which describe an operation that swap $$$a_{x_i, z_i}, a_{y_i, z_i}$$$: swap the $$$z_i$$$-th number of the $$$x_i$$$-th and $$$y_i$$$-th arrays.

Sample Input:

3
3 4
1 1 1 0
0 0 1 0
1 0 0 1
4 3
1 0 0
0 1 1
0 0 1
0 0 0
2 2
0 0
0 1

Sample Output:

1
2 1 1
1
4 2 2
-1

Note:

In the first test case, it's enough to do a single operation: to swap the first element in the second and the first rows. The arrays will become $$$[0, 1, 1, 0], [1, 0, 1, 0], [1, 0, 0, 1]$$$, each of them contains exactly two $$$1$$$s.