A two dimensional array is called a bracket array if each grid contains one of the two possible brackets — "(" or ")". A path through the two dimensional array cells is called monotonous if any two consecutive cells in the path are side-adjacent and each cell of the path is located below or to the right from the previous one. 

A two dimensional array whose size equals n × m is called a correct bracket array, if any string formed by writing out the brackets on some monotonous way from cell (1, 1) to cell (n, m) forms a correct bracket sequence. 

Let's define the operation of comparing two correct bracket arrays of equal size (a and b) like that. Let's consider a given two dimensional array of priorities (c) — a two dimensional array of same size, containing different integers from 1 to nm. Let's find such position (i, j) in the two dimensional array, that ai, j ≠ bi, j. If there are several such positions, let's choose the one where number ci, j is minimum. If ai, j = "(", then a < b, otherwise a > b. If the position (i, j) is not found, then the arrays are considered equal.

Your task is to find a k-th two dimensional correct bracket array. It is guaranteed that for the given sizes of n and m there will be no less than k two dimensional correct bracket arrays.

Input

The first line contains integers n, m and k — the sizes of the array and the number of the sought correct bracket array (1 ≤ n, m ≤ 100, 1 ≤ k ≤ 1018). Then an array of priorities is given, n lines each containing m numbers, number pi, j shows the priority of character j in line i (1 ≤ pi, j ≤ nm, all pi, j are different).

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Output

Print the k-th two dimensional correct bracket array.

Examples

Input

1 2 1
1 2


Output

()


Input

2 3 1
1 2 3
4 5 6


Output

(()
())


Input

3 2 2
3 6
1 4
2 5


Output

()
)(
()

Note

In the first sample exists only one correct two-dimensional bracket array.

In the second and in the third samples two arrays exist.

A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters «+» and «1» into this sequence. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.
import java.awt.geom.*;
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.regex.*;
import static java.lang.Math.*;
public class C {

    int n;
    int m;
    long k;

    public C() throws Exception {
        n = in.nextInt();
        m = in.nextInt();
        k = in.nextLong();

        int[] p = new int[n+m-1];
        Arrays.fill(p, 1<<30);
        for (int r=0;r<n;r++)
            for (int c=0;c<m;c++)
                p[r+c] = min(p[r+c], in.nextInt());

        char[] s = new char[n+m-1];
        for (int l=0;l<n+m-1;l++) {
            int min = 1<<30;
            int index = 0;
            for (int i=0;i<n+m-1;i++) {
                if (s[i]!=0) continue;
                if (min>p[i]) {
                    min = p[i];
                    index = i;
                }
            }

            s[index] = '(';
            long[][] dp = new long[n+m][n+m];
            dp[0][0] = 1;
            for (int i=0;i<n+m-1;i++) {
                for (int j=i&1;j<=i&&j<=n+m-1-i;j+=2) {
                    if (dp[i][j]>k) dp[i][j] = k;
                    if (s[i]!=')') dp[i+1][j+1] += dp[i][j];
                    if (s[i]!='('&&j>0) dp[i+1][j-1] += dp[i][j];
                }
            }
            
            if (k>dp[n+m-1][0]) {
                k -= dp[n+m-1][0];
                s[index] = ')';
            }
        }

        for (int r=0;r<n;r++) {
            for (int c=0;c<m;c++)
                buf.append(s[r+c]);
            buf.append('\n');
        }
                
        System.out.print(buf);
    }

    Scanner in = new Scanner(System.in);
    StringBuilder buf = new StringBuilder();
    public static void main(String[] args) throws Exception { // {{{
        new C();
    } // }}}
    public static void debug(Object... arr) { // {{{
        System.err.println(Arrays.deepToString(arr));
    } // }}}
}
