Problem: Pink Floyd are pulling a prank on Roger Waters. They know he doesn't like [walls](https://www.youtube.com/watch?v=YR5ApYxkU-U), 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× 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

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 50). Description of the test cases follows.

The first line of each test case contains one integers n (3 ≤ n ≤ 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

For each test case output on the first line an integer c (0 ≤ c ≤ 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).

Example

Input


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


Output


1
3 4
2
1 2
2 1
0

Note

For the first test case, after inverting the cell, we get the following grid:
    
    
      
    S010  
    0001  
    1001  
    111F  
    

Solution (in JAVA):

Solution:

import java.awt.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.util.List;

/**
 * Codeforces
 * 
 * 
 */
public class Codeforcess {

    public static boolean has1inbetween(String s, int i, int j) {
        boolean ans = true;
        char ch[] = s.toCharArray();

        for (int b = i + 1; b < j && b < s.length() && i < ch.length && j < ch.length; b++) {
            if (ch[i] == '1') {
                ans = false;
            }
        }
        return ans;
    }

    public static int segregate(int arr[], int size) {
        int j = 0, i;
        for (i = 0; i < size; i++) {
            if (arr[i] <= 0) {
                int temp;
                temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
                // increment count of non-positive
                // integers
                j++;
            }
        }

        return j;
    }

    public static long lowComMultiple(long a, long b) {
        long min = a * b;
        long start = Math.min(a, b);
        long ans = -1;
        for (int i = (int) start; i <= min; i++) {
            if (i % a == 0 && i % b == 0) {
                ans = i;
                break;
            }
        }
        return ans;
    }

    public static int solution(int[] A) {
        int n = A.length;

        // To mark the occurrence of elements
        boolean[] present = new boolean[n + 1];

        // Mark the occurrences
        for (int i = 0; i < n; i++) {

            if (A[i] > 0 && A[i] <= n)
                present[A[i]] = true;
        }

        // Find the first element which didn't
        // appear in the original array
        for (int i = 1; i <= n; i++)
            if (!present[i])
                return i;

        return n + 1;
    }

    public static ArrayList<Long> digit(long num) {
        long dig = 0;
        // long length = 0;
        ArrayList<Long> digi = new ArrayList<>();
        while (num > 0) {
            dig = num % 10;
            digi.add(dig);
            num = num / 10;

        }
        // return dig; //System.out.printf("%d", +revnum);

        return digi;
    }

    static int[] shuffle(int a[], int n) {
        for (int i = 0; i < n; i++) {

            // getting the random index
            int t = (int) Math.random() * a.length;

            // and swapping values a random index
            // with the current index
            int x = a[t];
            a[t] = a[i];
            a[i] = x;
        }
        return a;
    }

    public void dump() {

    }

    public static long addDigits(long num) {
        long digit = 0;
        // long sum = 0;
        long dig = -1;

        while (num != 0) {
            digit = num % 10;
            dig = digit;
            num = num / 10;
            break;
        }
        return dig;
    }

    public static int addDigit(long num) {
        long digit = 0;
        // long sum = 0;
        int count = 0;

        while (num != 0) {
            digit = num % 10;
            count++;
            num = num / 10;

        }
        return count;
    }

    public static class Pair<A, B> {
        private A first;
        private B second;

        public Pair(A first, B second) {
            this.first = first;
            this.second = second;
        }

        public A getFirst() {
            return first;
        }

        public B getSecond() {
            return second;
        }

        public void setFirst(A first) {
            this.first = first;
        }

        public void setSecond(B second) {
            this.second = second;
        }
    }

    public static void main(String[] args) {

        try {
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            Scanner sc = new Scanner(System.in);
            int T = sc.nextInt();
            while (T-- > 0) {
                int n = sc.nextInt();
                sc.nextLine();
                char[][] box = new char[n][n];
                for (int i = 0; i < n; i++) {
                    String row = sc.next();
                    char[] r = row.toCharArray();
                    box[i] = r;
                }

                int a = box[0][1];
                int b = box[1][0];
                int c = box[n - 1][n - 2];
                int d = box[n - 2][n - 1];

                Pair<Integer, Integer> p = new Pair<Integer, Integer>(0, 0);
                ArrayList<Pair<Integer, Integer>> ar = new ArrayList<>();

                if (a == b) {
                    if (c == a) {
                        p.setFirst(n);
                        p.setSecond(n - 1);
                        ar.add(p);
                    }
                    p = new Pair<Integer, Integer>(0, 0);
                    if (a == d) {
                        p.setFirst(n - 1);
                        p.setSecond(n);
                        ar.add(p);
                    }

                } else if (c == d) {
                    if (c == a) {
                        p.setFirst(1);
                        p.setSecond(2);
                        ar.add(p);
                    }
                    p = new Pair<Integer, Integer>(0, 0);
                    if (c == b) {
                        p.setFirst(2);
                        p.setSecond(1);
                        ar.add(p);
                    }
                } else {
                    p = new Pair<Integer, Integer>(0, 0);
                    p.setFirst(2);
                    p.setSecond(1);
                    ar.add(p);
                    p = new Pair<Integer, Integer>(0, 0);
                    if (c == a) {
                        p.setFirst(n);
                        p.setSecond(n - 1);
                        ar.add(p);
                    }
                    p = new Pair<Integer, Integer>(0, 0);
                    if (d == a) {
                        p.setFirst(n - 1);
                        p.setSecond(n);
                        ar.add(p);
                    }
                }
                System.out.println(ar.size());
                for (int i = 0; i < ar.size(); i++) {
                    System.out.println(ar.get(i).getFirst() + " " + ar.get(i).getSecond());
                }

            }
        } catch (Exception e) {
            System.out.println(e);
        }

    }

}