Putting Bricks in the Wall
Contest: Codeforces Round 676 (Div. 2)
Difficulty rating: 1100
Tags: constructive algorithms, implementation

Pink Floyd are pulling a prank on Roger Waters. They know he doesn't like walls, he wants to be able to walk freely, so they are blocking him from exiting his room which can be seen as a grid.

Roger Waters has a square grid of size $$$n\times n$$$ and he wants to traverse his grid from the upper left ($$$1,1$$$) corner to the lower right corner ($$$n,n$$$). Waters can move from a square to any other square adjacent by a side, as long as he is still in the grid. Also except for the cells ($$$1,1$$$) and ($$$n,n$$$) every cell has a value $$$0$$$ or $$$1$$$ in it.

Before starting his traversal he will pick either a $$$0$$$ or a $$$1$$$ and will be able to only go to cells values in which are equal to the digit he chose. The starting and finishing cells ($$$1,1$$$) and ($$$n,n$$$) are exempt from this rule, he may go through them regardless of picked digit. Because of this the cell ($$$1,1$$$) takes value the letter 'S' and the cell ($$$n,n$$$) takes value the letter 'F'.

For example, in the first example test case, he can go from ($$$1, 1$$$) to ($$$n, n$$$) by using the zeroes on this path: ($$$1, 1$$$), ($$$2, 1$$$), ($$$2, 2$$$), ($$$2, 3$$$), ($$$3, 3$$$), ($$$3, 4$$$), ($$$4, 4$$$)

The rest of the band (Pink Floyd) wants Waters to not be able to do his traversal, so while he is not looking they will invert at most two cells in the grid (from $$$0$$$ to $$$1$$$ or vice versa). They are afraid they will not be quick enough and asked for your help in choosing the cells.  Note that you cannot invert cells $$$(1, 1)$$$ and $$$(n, n)$$$.

We can show that there always exists a solution for the given constraints.

Also note that Waters will pick his digit of the traversal after the band has changed his grid, so he must not be able to reach ($$$n,n$$$) no matter what digit he picks.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 50$$$). Description of the test cases follows.

The first line of each test case contains one integers $$$n$$$ ($$$3 \le n \le 200$$$).

The following $$$n$$$ lines of each test case contain the binary grid, square ($$$1, 1$$$) being colored in 'S' and square ($$$n, n$$$) being colored in 'F'.

The sum of values of $$$n$$$ doesn't exceed $$$200$$$.

Output format:
For each test case output on the first line an integer $$$c$$$ ($$$0 \le c \le 2$$$)  — the number of inverted cells.

In $$$i$$$-th of the following $$$c$$$ lines, print the coordinates of the $$$i$$$-th cell you inverted. You may not invert the same cell twice.  Note that you cannot invert cells $$$(1, 1)$$$ and $$$(n, n)$$$.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
For the first test case, after inverting the cell, we get the following grid:

Example input:
3
4
S010
0001
1000
111F
3
S10
101
01F
5
S0101
00000
01111
11111
0001F

Example output:
1
3 4
2
1 2
2 1
0

Editorial:
Hint:
It's hard to use the two valuable switches somewhere in the middle of the grid, a much wiser choice would be to somehow block the S cell or the F cell. Perhaps you can set both neighbours of S to 1 to force Roger to pick 1.
Solution:
If we pick the neighbours of S to be 1 we can make the neighbours of F 0 and there would be no way to go from S to F. But this in the worst case takes 4 switches, to get down to 2 switches we can consider the other way around, making the S neighbours 0 and F neighbours 1. There must be a solution of the two with at most two switches and you won't get from S to F since you're forced to pick 1 (or 0) and can't get past the neighbours of F which are opposite.