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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Iterator;
import java.util.Collection;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskC {
        @SuppressWarnings("unchecked")
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int[][] a = in.readIntMatrix(n, m);

            Set<Integer>[] rowSet = new Set[n];
            Set<Integer>[] colSet = new Set[m];

            IntList[] row = new IntList[n];
            IntList[] col = new IntList[m];

            for (int i = 0; i < n; i++)
                row[i] = new IntList(m);
            for (int i = 0; i < m; i++)
                col[i] = new IntList(n);

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    row[i].add(a[i][j]);
                    col[j].add(a[i][j]);
                }
            }


            for (int i = 0; i < n; i++) {
                row[i].sortAndUnify();
            }

            for (int i = 0; i < m; i++) {
                col[i].sortAndUnify();
            }

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    if (j > 0) out.space();
                    int rowIndex = row[i].upperBound(a[i][j]);
                    int colIndex = col[j].upperBound(a[i][j]);
                    int value = Math.max(rowIndex, colIndex);
                    value += Math.max(row[i].size() - rowIndex, col[j].size() - colIndex);
                    out.print(value);
                }
                out.println();
            }
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

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

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = nextInt();
            return array;
        }

        public int[][] readIntMatrix(int n, int m) {
            int[][] matrix = new int[n][m];
            for (int i = 0; i < n; i++) {
                matrix[i] = readIntArray(m);
            }
            return matrix;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void space() {
            print(' ');
        }

        public void close() {
            super.close();
        }

    }

    static class IntList implements Iterable<Integer> {
        public static final int INITIAL_CAPACITY = 4;
        private int size;
        private int[] array;

        public IntList() {
            this(INITIAL_CAPACITY);
        }

        public IntList(int initialCapacity) {
            this.array = new int[initialCapacity];
            this.size = 0;
        }

        public IntList(int[] array) {
            this.array = Arrays.copyOf(array, array.length);
            this.size = this.array.length;
        }

        public IntList(Collection<Integer> collection) {
            this.size = collection.size();
            this.array = new int[size];
            int index = 0;
            for (int e : collection) {
                array[index++] = e;
            }
        }

        public void add(int value) {
            if (size == array.length) {
                ensureCapacity();
            }

            this.array[this.size++] = value;
        }

        public int upperBound(int value) {
            return upperBound(value, 0, size - 1);
        }

        private int upperBound(int value, int low, int high) {
            if (low < 0 || high >= size)
                throw new IllegalArgumentException("Invalid boundaries for lowerBound algorithm");

            while (low <= high) {
                int mid = low + high >> 1;
                if (array[mid] <= value)
                    low = mid + 1;
                else
                    high = mid - 1;
            }

            return high;
        }

        public void sortAndUnify() {
            if (size <= 1) return;

            Arrays.sort(array, 0, size);
            int uniqueSize = 1;
            for (int i = 1; i < size; i++) {
                if (array[i] != array[i - 1])
                    uniqueSize++;
            }

            int[] temp = new int[uniqueSize];
            temp[0] = array[0];
            for (int i = 1, j = 1; i < size; i++) {
                if (array[i] != array[i - 1])
                    temp[j++] = array[i];
            }

            array = temp;
            size = uniqueSize;
        }

        public int size() {
            return this.size;
        }

        private void ensureCapacity() {
            if (size < array.length)
                return;
            this.array = Arrays.copyOf(array, array.length << 1);
        }

        public IntList clone() {
            IntList cloned = new IntList(Math.max(1, this.size));
            for (int i = 0; i < size; ++i)
                cloned.add(array[i]);
            return cloned;
        }


        public Iterator<Integer> iterator() {
            return new IntListIterator();
        }

        private class IntListIterator implements Iterator<Integer> {
            private int current;

            public IntListIterator() {
                this.current = 0;
            }


            public boolean hasNext() {
                return this.current < size;
            }


            public Integer next() {
                return array[current++];
            }

        }

    }
}