Problem: Dora loves adventures quite a lot. During some journey she encountered an amazing city, which is formed by n streets along the Eastern direction and m streets across the Southern direction. Naturally, this city has nm intersections. At any intersection of i-th Eastern street and j-th Southern street there is a monumental skyscraper. Dora instantly became curious and decided to explore the heights of the city buildings.

When Dora passes through the intersection of the i-th Eastern and j-th Southern street she examines those two streets. After Dora learns the heights of all the skyscrapers on those two streets she wonders: how one should reassign heights to the skyscrapers on those two streets, so that the maximum height would be as small as possible and the result of comparing the heights of any two skyscrapers on one street wouldn't change.

Formally, on every of nm intersections Dora solves an independent problem. She sees n + m - 1 skyscrapers and for each of them she knows its real height. Moreover, any two heights can be compared to get a result "greater", "smaller" or "equal". Now Dora wants to select some integer x and assign every skyscraper a height from 1 to x. When assigning heights, Dora wants to preserve the relative order of the skyscrapers in both streets. That is, the result of any comparison of heights of two skyscrapers in the current Eastern street shouldn't change and the result of any comparison of heights of two skyscrapers in current Southern street shouldn't change as well. Note that skyscrapers located on the Southern street are not compared with skyscrapers located on the Eastern street only. However, the skyscraper located at the streets intersection can be compared with both Southern and Eastern skyscrapers. For every intersection Dora wants to independently calculate the minimum possible x.

For example, if the intersection and the two streets corresponding to it look as follows:

<image>

Then it is optimal to replace the heights of the skyscrapers as follows (note that all comparisons "less", "equal", "greater" inside the Eastern street and inside the Southern street are preserved)

<image>

The largest used number is 5, hence the answer for this intersection would be 5.

Help Dora to compute the answers for each intersection.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 1000) — the number of streets going in the Eastern direction and the number of the streets going in Southern direction.

Each of the following n lines contains m integers a_{i,1}, a_{i,2}, ..., a_{i,m} (1 ≤ a_{i,j} ≤ 10^9). The integer a_{i,j}, located on j-th position in the i-th line denotes the height of the skyscraper at the intersection of the i-th Eastern street and j-th Southern direction.

Output

Print n lines containing m integers each. The integer x_{i,j}, located on j-th position inside the i-th line is an answer for the problem at the intersection of i-th Eastern street and j-th Southern street.

Examples

Input


2 3
1 2 1
2 1 2


Output


2 2 2 
2 2 2 


Input


2 2
1 2
3 4


Output


2 3 
3 2 

Note

In the first example, it's not possible to decrease the maximum used height for the problem at any intersection, hence we don't have to change any heights.

In the second example, the answers are as follows: 

  * For the intersection of the first line and the first column <image>
  * For the intersection of the first line and the second column <image>
  * For the intersection of the second line and the first column <image>
  * For the intersection of the second line and the second column <image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 *
 * @author pttrung
 */
public class C_Round_545_Div2 {

    public static long MOD = 998244353;
    static long[][][] dp;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int m = in.nextInt();
        int[][] data = new int[n][m];
        HashSet<Integer>[] row = new HashSet[n];
        HashSet<Integer>[] col = new HashSet[m];
        for (int i = 0; i < n; i++) {
            row[i] = new HashSet<>();
        }
        for (int i = 0; i < m; i++) {
            col[i] = new HashSet<>();
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                data[i][j] = in.nextInt();
                row[i].add(data[i][j]);
                col[j].add(data[i][j]);
            }
        }
        int[][] r = new int[n][];
        int[][] c = new int[m][];

        for (int i = 0; i < n; i++) {
            r[i] = new int[row[i].size()];
            int index = 0;
            for (int j : row[i]) {
                r[i][index++] = j;
            }

            Arrays.sort(r[i]);
        }
        for (int i = 0; i < m; i++) {
            c[i] = new int[col[i].size()];
            int index = 0;
            for (int j : col[i]) {
                c[i][index++] = j;
            }
            Arrays.sort(c[i]);
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                int a = smaller(data[i][j], r[i]);
                int b = r[i].length - a - 1;
                int x = smaller(data[i][j], c[j]);
                int y = c[j].length - x - 1;
                int re = 1 + Integer.max(a, x) + Integer.max(b, y);
                //System.out.println(data[i][j] + " " + Arrays.toString(r[i]) + " " + Arrays.toString(c[j]) + " " + a + " " + b + " " + x + " " + y);
                out.print(re + " ");
            }
            out.println();
        }
        out.close();
    }

    static int smaller(int v, int[] data) {
        int st = 0;
        int ed = data.length - 1;
        int re = 0;
        while (st <= ed) {
            int mid = (st + ed) / 2;
            if (data[mid] < v) {
                re = mid + 1;
                st = mid + 1;
            } else {
                ed = mid - 1;
            }
        }
        return re;
    }

    static int larger(int v, int st, int[] data) {

        int ed = data.length - 1;
        int re = 0;
        while (st <= ed) {
            int mid = (st + ed) / 2;
            if (data[mid] > v) {
                re = data.length - mid;
                ed = mid - 1;
            } else {
                st = mid + 1;
            }
        }
        return re;
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}