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.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;
public class Main {
    static long MAX = 1000000000000000000L;
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        long k = scanner.nextLong();
        int a[][] = new int[n][m];
        final int dp[] = new int[n+m- 1];
        List<Integer> pos = new ArrayList<Integer>();
        pos.clear();
        for (int i = 0; i <dp.length; i ++) {
            pos.add(i);
            dp[i] = 0;
        }
        for (int i = 0; i < n; i ++) {
            for (int j = 0; j < m; j ++) {
                a[i][j] = scanner.nextInt();
                dp[i + j] = Math.max(dp[i + j], a[i][j]);
            }
        }
        for (int i = 0; i < n; i ++) {
            for (int j = 0; j <m; j ++) dp[i + j] = Math.min(dp[i + j], a[i][j]);
        }
        Compare cmp = new Compare(dp);        
        Collections.sort(pos,cmp);
        char ans[] = new char[dp.length];
        Arrays.fill(ans, '_');
        for (int i = 0; i < dp.length; i ++) {
            //if (ans[pos.get(i)] != '_') continue;
            ans[pos.get(i)] = '(';
            long tp = cal(ans);
            if (tp < k)  {
                k -= tp;
                ans[pos.get(i)] = ')';
            }            
        }
        for (int i = 0; i < n; i ++) {
            for (int j = 0; j < m;j ++) {
                System.out.print(ans[i+j]);
            }
            System.out.println();
        }
        
    }
    public static long cal(char ans[]) {
        
        int n = ans.length;
        long dp[][] = new long[n][n];
        for(int i = 0; i < n; i ++) {
            for (int j = 0; j < n; j ++) dp[i][j] = 0;
        }
        dp[0][1] = 1;
        boolean flag1 ,flag2;
        boolean flag[][] = new boolean[n][n];
        for (int i = 0; i + 1 < n; i ++) {
            for (int j =  0; j < n; j ++) {
                if (dp[i][j]> 0) {
                    flag1 = flag2 = false;
                    if (ans[i + 1] == '(' || ans[i + 1] == '_') flag1 = true;
                    if (ans[i + 1] == ')' || ans[i + 1] == '_') flag2 = true;
                    if (flag1 && j +1 < n) {
                        
                        dp[i+1][j+1] += dp[i][j];
                        if (dp[i+1][j+1] > MAX) dp[i+1][j+1] = MAX;
                    } 
                    if (flag2 && j > 0) {
                        dp[i+1][j-1] += dp[i][j];
                        if (dp[i+1][j-1] > MAX) dp[i+1][j-1] = MAX;
                        
                    }
                }
            }
        }
        return dp[n - 1][0];
    }

}

class Compare implements Comparator<Integer> {
    int[] a;
    public Compare(int a[]) {
        this.a = a;
    }

    @Override
    public int compare(Integer arg0, Integer arg1) {
        return a[arg0] - a[arg1];
    }
    
}
