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.io.*;
import java.util.*;
import java.util.stream.IntStream;

import static java.lang.Math.*;
import static java.util.Arrays.*;

@SuppressWarnings("ALL")
public class TaskB {
    public static void main(String[] $) throws IOException {
        TaskB o = new TaskB();
        o.main();
        out.flush();
        out.close();
    }

    Scanner sc = new Scanner(System.in);

    void main() throws IOException {
        int T = sc.nextInt();
        while (T-- > 0) {
            int n = sc.nextInt();
            char[][] a = new char[n][n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.next().toCharArray();
            }

            if (a[0][1] == a[1][0]) {
                if (a[n - 1][n - 2] == a[0][1] && a[n - 2][n - 1] == a[0][1]) {
                    out.prln(2);
                    out.prln("1 2");
                    out.prln("2 1");
                }
                if (a[n - 1][n - 2] != a[0][1] && a[n - 2][n - 1] != a[0][1]) {
                    out.prln(0);
                }
                if (a[n - 1][n - 2] != a[n - 2][n - 1]) {
                    if (a[n - 1][n - 2] == a[0][1]) {
                        out.prln(1);
                        out.prln((n - 1 + 1) + " " + (n - 2 + 1));
                    } else if (a[n - 2][n - 1] == a[0][1]) {
                        out.prln(1);
                        out.prln((n - 2 + 1) + " " + (n - 1 + 1));
                    }
                }
            }

            if (a[0][1] != a[1][0]) {
                if (a[n - 1][n - 2] == a[n - 2][n - 1]) {
                    if (a[0][1] == a[n - 1][n - 2]) {
                        out.prln(1);
                        out.prln("1 2");
                    }
                    if (a[1][0] == a[n - 1][n - 2]) {
                        out.prln(1);
                        out.prln("2 1");
                    }
                }
                if (a[n - 1][n - 2] != a[n - 2][n - 1]) {
                    int count = 0;
                    StringBuilder sb = new StringBuilder();
                    if (a[0][1] == '0') {
                        count++;
                        sb.append("1 2").append("\n");
                    } else if (a[1][0] == '0') {
                        count++;
                        sb.append("2 1").append("\n");
                    }
                    if (a[n - 1][n - 2] == '1') {
                        count++;
                        sb.append((n - 1 + 1) + " " + (n - 2 + 1)).append("\n");
                    } else if(a[n - 2][n - 1] == '1'){
                        count++;
                        sb.append((n - 2 + 1) + " " + (n - 1 + 1)).append("\n");
                    }
                    out.prln(count);
                    out.prln(sb);
                }
            }

        }
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();
    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;

    //Fast Reader Class
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    //Input fxs
    static class in {
        // input
        static void r() throws IOException {
            input = new StringTokenizer(rline());
        }

        static int ri() throws IOException {
            return Integer.parseInt(rline());
        }

        static long rl() throws IOException {
            return Long.parseLong(rline());
        }

        static double rd() throws IOException {
            return Double.parseDouble(rline());
        }

        static int[] ria(int n) throws IOException {
            int[] a = new int[n];
            r();
            for (int i = 0; i < n; ++i) a[i] = ni();
            return a;
        }

        static int[] riam1(int n) throws IOException {
            int[] a = new int[n];
            r();
            for (int i = 0; i < n; ++i) a[i] = ni() - 1;
            return a;
        }

        static long[] ria1i(long n) throws IOException {
            long[] a = new long[(int) n + 1];
            r();
            for (int i = 1; i <= n; i++) a[i] = nl();
            return a;
        }

        static long[] rla(int n) throws IOException {
            long[] a = new long[n];
            r();
            for (int i = 0; i < n; ++i) a[i] = nl();
            return a;
        }

        static double[] rda(int n) throws IOException {
            double[] a = new double[n];
            r();
            for (int i = 0; i < n; ++i) a[i] = nd();
            return a;
        }

        static char[] rcha() throws IOException {
            return rline().toCharArray();
        }

        static ArrayList<Integer> riaa(int n) throws IOException {
            ArrayList<Integer> a = new ArrayList<>();
            r();
            for (int i = 0; i < n; i++) a.add(ni());
            return a;
        }

        static String rline() throws IOException {
            return __in.readLine();
        }

        static String n() {
            return input.nextToken();
        }

        static int rni() throws IOException {
            r();
            return ni();
        }

        static int ni() {
            return Integer.parseInt(n());
        }

        static long rnl() throws IOException {
            r();
            return nl();
        }

        static long nl() {
            return Long.parseLong(n());
        }

        static double rnd() throws IOException {
            r();
            return nd();
        }

        static double nd() {
            return Double.parseDouble(n());
        }

        static List<List<Integer>> rg(int n, int m) throws IOException {
            List<List<Integer>> g = GR.g(n);
            for (int i = 0; i < m; ++i) GR.c(g, rni() - 1, ni() - 1);
            return g;
        }

        static void rg(List<List<Integer>> g, int m) throws IOException {
            for (int i = 0; i < m; ++i) GR.c(g, rni() - 1, ni() - 1);
        }

        static List<List<Integer>> rdg(int n, int m) throws IOException {
            List<List<Integer>> g = GR.g(n);
            for (int i = 0; i < m; ++i) GR.cto(g, rni() - 1, ni() - 1);
            return g;
        }

        static void rdg(List<List<Integer>> g, int m) throws IOException {
            for (int i = 0; i < m; ++i) GR.cto(g, rni() - 1, ni() - 1);
        }

        static List<Set<Integer>> rsg(int n, int m) throws IOException {
            List<Set<Integer>> g = GR.sg(n);
            for (int i = 0; i < m; ++i) GR.c(g, rni() - 1, ni() - 1);
            return g;
        }

        static void rsg(List<Set<Integer>> g, int m) throws IOException {
            for (int i = 0; i < m; ++i) GR.c(g, rni() - 1, ni() - 1);
        }

        static List<Set<Integer>> rdsg(int n, int m) throws IOException {
            List<Set<Integer>> g = GR.sg(n);
            for (int i = 0; i < m; ++i) GR.cto(g, rni() - 1, ni() - 1);
            return g;
        }

        static void rdsg(List<Set<Integer>> g, int m) throws IOException {
            for (int i = 0; i < m; ++i) GR.cto(g, rni() - 1, ni() - 1);
        }

        static String[][] rim(int n, int m) throws IOException {
            String[][] a = new String[n][m];
            for (int i = 0; i < n; i++) {
                in.r();
                for (int j = 0; j < m; j++) {
                    a[i][j] = n();
                }
            }
            return a;
        }
    }

    //Output fxs
    static class out {
        // output
        static void pr(int i) {
            __out.print(i);
        }

        static void prln(int i) {
            __out.println(i);
        }

        static void pr(long l) {
            __out.print(l);
        }

        static void prln(long l) {
            __out.println(l);
        }

        static void pr(double d) {
            __out.print(d);
        }

        static void prln(double d) {
            __out.println(d);
        }

        static void pr(char c) {
            __out.print(c);
        }

        static void prln(char c) {
            __out.println(c);
        }

        static void pr(char[] s) {
            __out.print(new String(s));
        }

        static void prln(char[] s) {
            __out.println(new String(s));
        }

        static void pr(String s) {
            __out.print(s);
        }

        static void prln(String s) {
            __out.println(s);
        }

        static void pr(Object o) {
            __out.print(o);
        }

        static void prln(Object o) {
            __out.println(o);
        }

        static void prln() {
            __out.println();
        }

        static void pryes() {
            prln("yes");
        }

        static void pry() {
            prln("Yes");
        }

        static void prY() {
            prln("YES");
        }

        static void prno() {
            prln("no");
        }

        static void prn() {
            prln("No");
        }

        static void prN() {
            prln("NO");
        }

        static void pryesno(boolean b) {
            prln(b ? "yes" : "no");
        }

        ;

        static void pryn(boolean b) {
            prln(b ? "Yes" : "No");
        }

        static void prYN(boolean b) {
            prln(b ? "YES" : "NO");
        }

        static void prln(int... a) {
            for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
            if (a.length > 0) prln(a[a.length - 1]);
            else prln();
        }

        static void prln(long... a) {
            for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
            if (a.length > 0) prln(a[a.length - 1]);
            else prln();
        }

        static void prln(double... a) {
            for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i) ;
            if (a.length > 0) prln(a[a.length - 1]);
            else prln();
        }

        static <T> void prln(Collection<T> c) {
            int n = c.size() - 1;
            Iterator<T> iter = c.iterator();
            for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i) ;
            if (n >= 0) prln(iter.next());
            else prln();
        }

        static void h() {
            prln("hlfd");
            flush();
        }

        static void flush() {
            __out.flush();
        }

        static void close() {
            __out.close();
        }

        static void prM(int[][] a, int n, int m) {
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++)
                    out.pr(a[i][j] + " ");
                out.prln();
            }
        }
    }

    //Math fxs
    static class mathx {
        // math util
        static int minof(int a, int b, int c) {
            return min(a, min(b, c));
        }

        static int minof(int... x) {
            if (x.length == 1) return x[0];
            if (x.length == 2) return min(x[0], x[1]);
            if (x.length == 3) return min(x[0], min(x[1], x[2]));
            int min = x[0];
            for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
            return min;
        }

        static long minof(long a, long b, long c) {
            return min(a, min(b, c));
        }

        static long minof(long... x) {
            if (x.length == 1) return x[0];
            if (x.length == 2) return min(x[0], x[1]);
            if (x.length == 3) return min(x[0], min(x[1], x[2]));
            long min = x[0];
            for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i];
            return min;
        }

        static int maxof(int a, int b, int c) {
            return max(a, max(b, c));
        }

        static int maxof(int... x) {
            if (x.length == 1) return x[0];
            if (x.length == 2) return max(x[0], x[1]);
            if (x.length == 3) return max(x[0], max(x[1], x[2]));
            int max = x[0];
            for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
            return max;
        }

        static long maxof(long a, long b, long c) {
            return max(a, max(b, c));
        }

        static long maxof(long... x) {
            if (x.length == 1) return x[0];
            if (x.length == 2) return max(x[0], x[1]);
            if (x.length == 3) return max(x[0], max(x[1], x[2]));
            long max = x[0];
            for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i];
            return max;
        }

        static int powi(int a, int b) {
            if (a == 0) return 0;
            int ans = 1;
            while (b > 0) {
                if ((b & 1) > 0) ans *= a;
                a *= a;
                b >>= 1;
            }
            return ans;
        }

        static long powl(long a, int b) {
            if (a == 0) return 0;
            long ans = 1;
            while (b > 0) {
                if ((b & 1) > 0) ans *= a;
                a *= a;
                b >>= 1;
            }
            return ans;
        }

        static int fli(double d) {
            return (int) d;
        }

        static int cei(double d) {
            return (int) ceil(d);
        }

        static long fll(double d) {
            return (long) d;
        }

        static long cel(double d) {
            return (long) ceil(d);
        }

        static int gcf(int a, int b) {
            return b == 0 ? a : gcf(b, a % b);
        }

        static long gcf(long a, long b) {
            return b == 0 ? a : gcf(b, a % b);
        }

        static int lcm(int a, int b) {
            return a * b / gcf(a, b);
        }

        static long lcm(long a, long b) {
            return a * b / gcf(a, b);
        }

        static int randInt(int min, int max) {
            return __rand.nextInt(max - min + 1) + min;
        }

        static long mix(long x) {
            x += 0x9e3779b97f4a7c15L;
            x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L;
            x = (x ^ (x >> 27)) * 0x94d049bb133111ebL;
            return x ^ (x >> 31);
        }
    }

    //Array fxs
    static class ARR {
        // array util
        static void reverse(int[] a) {
            for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
                int swap = a[i];
                a[i] = a[n - i - 1];
                a[n - i - 1] = swap;
            }
        }

        static void reverse(long[] a) {
            for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
                long swap = a[i];
                a[i] = a[n - i - 1];
                a[n - i - 1] = swap;
            }
        }

        static void reverse(double[] a) {
            for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
                double swap = a[i];
                a[i] = a[n - i - 1];
                a[n - i - 1] = swap;
            }
        }

        static void reverse(char[] a) {
            for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {
                char swap = a[i];
                a[i] = a[n - i - 1];
                a[n - i - 1] = swap;
            }
        }

        static void shuffle(int[] a) {
            int n = a.length - 1;
            for (int i = 0; i < n; ++i) {
                int ind = mathx.randInt(i, n);
                int swap = a[i];
                a[i] = a[ind];
                a[ind] = swap;
            }
        }

        static void shuffle(long[] a) {
            int n = a.length - 1;
            for (int i = 0; i < n; ++i) {
                int ind = mathx.randInt(i, n);
                long swap = a[i];
                a[i] = a[ind];
                a[ind] = swap;
            }
        }

        static void shuffle(double[] a) {
            int n = a.length - 1;
            for (int i = 0; i < n; ++i) {
                int ind = mathx.randInt(i, n);
                double swap = a[i];
                a[i] = a[ind];
                a[ind] = swap;
            }
        }

        static void rsort(int[] a) {
            shuffle(a);
            sort(a);
        }

        static void rsort(long[] a) {
            shuffle(a);
            sort(a);
        }

        static void rsort(double[] a) {
            shuffle(a);
            sort(a);
        }

        static int[] copy(int[] a) {
            int[] ans = new int[a.length];
            System.arraycopy(a, 0, ans, 0, a.length);
            return ans;
        }

        static long[] copy(long[] a) {
            long[] ans = new long[a.length];
            System.arraycopy(a, 0, ans, 0, a.length);
            return ans;
        }

        static double[] copy(double[] a) {
            double[] ans = new double[a.length];
            System.arraycopy(a, 0, ans, 0, a.length);
            return ans;
        }

        static char[] copy(char[] a) {
            char[] ans = new char[a.length];
            System.arraycopy(a, 0, ans, 0, a.length);
            return ans;
        }
    }

    //Graph fxs
    static class GR {
        // graph util
        static List<List<Integer>> g(int n) {
            List<List<Integer>> g = new ArrayList<>();
            for (int i = 0; i < n; ++i) g.add(new ArrayList<>());
            return g;
        }

        static List<Set<Integer>> sg(int n) {
            List<Set<Integer>> g = new ArrayList<>();
            for (int i = 0; i < n; ++i) g.add(new HashSet<>());
            return g;
        }

        static void c(List<? extends Collection<Integer>> g, int u, int v) {
            g.get(u).add(v);
            g.get(v).add(u);
        }

        static void cto(List<? extends Collection<Integer>> g, int u, int v) {
            g.get(u).add(v);
        }

        static void dc(List<? extends Collection<Integer>> g, int u, int v) {
            g.get(u).remove(v);
            g.get(v).remove(u);
        }

        static void dcto(List<? extends Collection<Integer>> g, int u, int v) {
            g.get(u).remove(v);
        }
    }

    //Utilsx class
    static class utilX {
        static int[] subsetSum(int[] nums) {
            int M = IntStream.of(nums).sum();
            int[] m = new int[M + 10];
            for (int i = 0; i < M + 10; i++) m[i] = 0;
            m[0] = 1;
            for (int num : nums) {
                for (int j = M; j >= num; j--) {
                    m[j] |= m[j - num];
                }
            }
            return m;
        }

        static int LIS(int[] nums) {
            int[] m = new int[nums.length];
            for (int i = nums.length - 1; i >= 0; i--) {
                m[i] = 1;
                for (int j = i + 1; j < nums.length; j++) {
                    if (nums[j] > nums[i]) {
                        m[i] = max(m[i], m[j] + 1);
                    }
                }
            }
            int ans = 0;
            for (int i = 0; i < nums.length; i++) {
                ans = max(ans, m[i]);
            }
            return ans;
        }
    }

    //Pair Class
    static class Pair<F, S> {
        public final F first;
        public final S second;

        public Pair(F first, S second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public boolean equals(Object o) {
            if (!(o instanceof Pair)) {
                return false;
            }
            Pair<?, ?> p = (Pair<?, ?>) o;
            return Objects.equals(p.first, first) && Objects.equals(p.second, second);
        }
    }
}