Problem: This is the hard version of the problem. The difference between the versions is in the number of possible operations that can be made. You can make hacks if and only if you solved both versions of the problem.

You are given a binary table of size n × m. This table consists of symbols 0 and 1.

You can make such operation: select 3 different cells that belong to one 2 × 2 square and change the symbols in these cells (change 0 to 1 and 1 to 0).

Your task is to make all symbols in the table equal to 0. You are allowed to make at most nm operations. You don't need to minimize the number of operations.

It can be proved, that it is always possible.

Input

The first line contains a single integer t (1 ≤ t ≤ 5000) — the number of test cases. The next lines contain descriptions of test cases.

The first line of the description of each test case contains two integers n, m (2 ≤ n, m ≤ 100).

Each of the next n lines contains a binary string of length m, describing the symbols of the next row of the table.

It is guaranteed, that the sum of nm for all test cases does not exceed 20000.

Output

For each test case print the integer k (0 ≤ k ≤ nm) — the number of operations.

In the each of the next k lines print 6 integers x_1, y_1, x_2, y_2, x_3, y_3 (1 ≤ x_1, x_2, x_3 ≤ n, 1 ≤ y_1, y_2, y_3 ≤ m) describing the next operation. This operation will be made with three cells (x_1, y_1), (x_2, y_2), (x_3, y_3). These three cells should be different. These three cells should belong to some 2 × 2 square.

Example

Input


5
2 2
10
11
3 3
011
101
110
4 4
1111
0110
0110
1111
5 5
01011
11001
00010
11011
10000
2 3
011
101


Output


1
1 1 2 1 2 2
2 
2 1 3 1 3 2
1 2 1 3 2 3
4
1 1 1 2 2 2 
1 3 1 4 2 3
3 2 4 1 4 2
3 3 4 3 4 4
4
1 2 2 1 2 2 
1 4 1 5 2 5 
4 1 4 2 5 1
4 4 4 5 3 4
2
1 3 2 2 2 3
1 2 2 1 2 2

Note

In the first test case, it is possible to make only one operation with cells (1, 1), (2, 1), (2, 2). After that, all symbols will be equal to 0.

In the second test case:

  * operation with cells (2, 1), (3, 1), (3, 2). After it the table will be: 
    
          
    011  
    001  
    000  
    

  * operation with cells (1, 2), (1, 3), (2, 3). After it the table will be: 
    
          
    000  
    000  
    000  
    




In the fifth test case:

  * operation with cells (1, 3), (2, 2), (2, 3). After it the table will be: 
    
          
    010  
    110  
    

  * operation with cells (1, 2), (2, 1), (2, 2). After it the table will be: 
    
          
    000  
    000  
    

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

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

public class cf1439a1 {

    public static void main(String[] args) throws IOException {
        int t = ri();
        while (t --> 0) {
            int n = rni(), m = ni(), mat[][] = new int[n][m];
            for (int i = 0; i < n; ++i) {
                char[] s = rcha();
                for (int j = 0; j < m; ++j) {
                    mat[i][j] = s[j] - '0';
                }
            }
            List<int[]> ans = new ArrayList<>();
            for (int i = 0; i < n - 1; ++i) {
                for (int j = 0; j < m - 1; ++j) {
                    if (j == m - 2) {
                        if (i == n - 2) {
                            int cnt = mat[i][j] + mat[i][j + 1] + mat[i + 1][j] + mat[i + 1][j + 1];
                            if (cnt == 4) {
                                apply(new int[] {i + 1, j + 1, i + 1, j + 2, i + 2, j + 1}, mat, ans);
                                apply(new int[] {i + 1, j + 2, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                                apply(new int[] {i + 1, j + 1, i + 1, j + 2, i + 2, j + 2}, mat, ans);
                                apply(new int[] {i + 1, j + 1, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                            } else if (cnt == 3) {
                                int ind = 0, move[] = new int[6];
                                for (int x = 0; x < 2; ++x) {
                                    for (int y = 0; y < 2; ++y) {
                                        if (mat[i + x][j + y] == 1) {
                                            move[ind++] = i + x + 1;
                                            move[ind++] = j + y + 1;
                                        }
                                    }
                                }
                                apply(move, mat, ans);
                            } else if (cnt == 2) {
                                int p[][] = new int[4][2], ai = 0, bi = 0;
                                for (int x = 0; x < 2; ++x) {
                                    for (int y = 0; y < 2; ++y) {
                                        if (mat[i + x][y + j] == 1) {
                                            p[ai][0] = i + x + 1;
                                            p[ai++][1] = j + y + 1;
                                        } else {
                                            p[2 + bi][0] = i + x + 1;
                                            p[2 + bi++][1] = j + y + 1;
                                        }
                                    }
                                }
                                apply(new int[] {p[2][0], p[2][1], p[3][0], p[3][1], p[0][0], p[0][1]}, mat, ans);
                                apply(new int[] {p[2][0], p[2][1], p[3][0], p[3][1], p[1][0], p[1][1]}, mat, ans);
                            } else if (cnt == 1) {
                                int p[][] = new int[4][2], bi = 0;
                                for (int x = 0; x < 2; ++x) {
                                    for (int y = 0; y < 2; ++y) {
                                        if (mat[i + x][y + j] == 1) {
                                            p[0][0] = i + x + 1;
                                            p[0][1] = j + y + 1;
                                        } else {
                                            p[1 + bi][0] = i + x + 1;
                                            p[1 + bi++][1] = j + y + 1;
                                        }
                                    }
                                }
                                apply(new int[] {p[0][0], p[0][1], p[1][0], p[1][1], p[2][0], p[2][1]}, mat, ans);
                                apply(new int[] {p[0][0], p[0][1], p[1][0], p[1][1], p[3][0], p[3][1]}, mat, ans);
                                apply(new int[] {p[0][0], p[0][1], p[2][0], p[2][1], p[3][0], p[3][1]}, mat, ans);
                            }
                        } else if (mat[i][j] == 1 && mat[i][j + 1] == 0) {
                            apply(new int[] {i + 1, j + 1, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                        } else if (mat[i][j] == 1 && mat[i][j + 1] == 1) {
                            apply(new int[] {i + 1, j + 1, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                            apply(new int[] {i + 1, j + 2, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                        } else if (mat[i][j] == 0 && mat[i][j + 1] == 1) {
                            apply(new int[] {i + 1, j + 2, i + 2, j + 1, i + 2, j + 2}, mat, ans);
                        }
                    } else if(i == n - 2) {
                        if (mat[i][j] == 1 && mat[i + 1][j] == 0) {
                            apply(new int[] {i + 1, j + 1, i + 1, j + 2, i + 2, j + 2}, mat, ans);
                        } else if (mat[i][j] == 1 && mat[i + 1][j] == 1) {
                            apply(new int[] {i + 1, j + 1, i + 1, j + 2, i + 2, j + 2}, mat, ans);
                            apply(new int[] {i + 2, j + 1, i + 1, j + 2, i + 2, j + 2}, mat, ans);
                        } else if (mat[i][j] == 0 && mat[i + 1][j] == 1) {
                            apply(new int[] {i + 2, j + 1, i + 1, j + 2, i + 2, j + 2}, mat, ans);
                        }
                    } else {
                        if (mat[i][j] == 1) {
                            apply(new int[] {i + 1, j + 1, i + 1, j + 2, i + 2, j + 1}, mat, ans);
                        }
                    }
                }
            }
            /* prln(ans.size() < n * m);
            for (int[] row : mat) {
                prln(row);
            } */
            prln(ans.size());
            for (int[] e : ans) {
                prln(e);
            }
        }
        close();
    }

    static void apply(int[] move, int[][] mat, List<int[]> list) {
        list.add(move);
        for (int i = 0; i < 3; ++i) {
            mat[move[i << 1] - 1][move[i << 1 | 1] - 1] = 1 - mat[move[i << 1] - 1][move[i << 1 | 1] - 1];
        }
    }

    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();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // 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;
    // 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 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 = 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 = 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 = 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]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    // 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[] 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 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());}
    // 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 boolean pryesno(boolean b) {prln(b ? "yes" : "no"); return b;};
    static boolean pryn(boolean b) {prln(b ? "Yes" : "No"); return b;}
    static boolean prYN(boolean b) {prln(b ? "YES" : "NO"); return b;}
    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();}
}