Problem: You are given a binary matrix a of size n × m. A binary matrix is a matrix where each element is either 0 or 1.

You may perform some (possibly zero) operations with this matrix. During each operation you can inverse the row of this matrix or a column of this matrix. Formally, inverting a row is changing all values in this row to the opposite (0 to 1, 1 to 0). Inverting a column is changing all values in this column to the opposite.

Your task is to sort the initial matrix by some sequence of such operations. The matrix is considered sorted if the array [a_{1, 1}, a_{1, 2}, ..., a_{1, m}, a_{2, 1}, a_{2, 2}, ..., a_{2, m}, ..., a_{n, m - 1}, a_{n, m}] is sorted in non-descending order.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 200) — the number of rows and the number of columns in the matrix.

The next n lines contain m integers each. The j-th element in the i-th line is a_{i, j} (0 ≤ a_{i, j} ≤ 1) — the element of a at position (i, j).

Output

If it is impossible to obtain a sorted matrix, print "NO" in the first line.

Otherwise print "YES" in the first line. In the second line print a string r of length n. The i-th character r_i of this string should be '1' if the i-th row of the matrix is inverted and '0' otherwise. In the third line print a string c of length m. The j-th character c_j of this string should be '1' if the j-th column of the matrix is inverted and '0' otherwise. If there are multiple answers, you can print any.

Examples

Input


2 2
1 1
0 1


Output


YES
00
10


Input


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


Output


YES
010
0000


Input


3 3
0 0 0
1 0 1
1 1 0


Output


NO

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mvv
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskG solver = new TaskG();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskG {
        private int n;
        private int m;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();
            int[][] origA = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    origA[i][j] = in.nextInt();
                }
            }
            if (n == 1) {
                out.println("YES");
                out.println(0);
                for (int j = 0; j < m; j++) {
                    out.print(origA[0][j]);
                }
                return;
            }

            if (m == 1) {
                out.println("YES");
                for (int j = 0; j < n; j++)
                    out.print(origA[j][0]);

                out.println();
                out.println(0);
                return;
            }
            int[][] a = new int[n][m];
            for (int i = 0; i <= m; i++) {
                for (int ii = 0; ii < n; ii++)
                    for (int jj = 0; jj < m; jj++)
                        a[ii][jj] = origA[ii][jj];

                int[] rows = new int[n];
                int[] columns = new int[m];
                for (int j = 0; j < m; j++) {
                    int p = (j < i) ? 0 : 1;
                    if (a[0][j] != p) {
                        reverseColumn(a, j);
                        columns[j] = 1;
                    }
                }
                boolean canTrig = (i == m) ? true : false;
                int cntChanges = 0;
                boolean isCont = false;
                for (int j = 1; j < n; j++) {
                    cntChanges = countChanges(a, j);
                    if (cntChanges > 1) {
                        isCont = true;
                        break;
                    }
                    if (cntChanges == 1 && !canTrig) {
                        isCont = true;
                        break;
                    }
                    if (cntChanges == 1) {
                        if (a[j][0] == 1) {
                            reverseRow(a, j);
                            rows[j] = 1;
                        }
                        canTrig = false;
                        continue;
                    }
                    if (canTrig && a[j][0] == 1 || !canTrig && a[j][0] == 0) {
                        reverseRow(a, j);
                        rows[j] = 1;
                    }
                }
                if (isCont) continue;

                out.println("YES");
                for (int r : rows)
                    out.print(r);
                out.println();
                for (int c : columns)
                    out.print(c);
                return;

            }
            out.print("NO");
        }

        private void reverseRow(int[][] a, int indRow) {
            for (int i = 0; i < m; i++)
                a[indRow][i] ^= 1;
        }

        private void reverseColumn(int[][] a, int indColumn) {
            for (int i = 0; i < n; i++)
                a[i][indColumn] ^= 1;
        }

        private int countChanges(int[][] a, int indRow) {
            int res = 0;
            for (int i = 1; i < m; i++)
                if (a[indRow][i - 1] != a[indRow][i]) res++;

            return res;

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}