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.io.*;
import java.util.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
public class Main{
    public static void main(String[]args){
        InputStream in = System.in;
        PrintWriter out = new PrintWriter(System.out);
        try{
            in = new BufferedInputStream(new FileInputStream(new File("input.txt")));
            out = new PrintWriter(new BufferedOutputStream(new FileOutputStream("output.txt")));
        }catch (Exception e) {
        }
        new Main().run(in,out);
        out.flush();
    }
    private void debug(Object...os){
        System.err.println(deepToString(os));
    }
    
    private void run(InputStream in,PrintWriter out){
//      test();
        int h=nextInt(in),w=nextInt(in);
        long k = nextLong(in);
        int[][] order=new int[h][w];
        for(int i=0;i<h;i++)for(int j=0;j<w;j++){
            order[i][j] = nextInt(in);
        }
        solve(h,w,k,order,out);
    }
    
    private void test() {
        int n = 100;
        int[] ord=new int[n];
        for(int i=0;i<n;i++)ord[i]=i;
        long k = 112098310284018L;
        String res = solve(ord, k);
        System.out.println(res);
    }
    private void solve(int h, int w, long k, int[][] order, PrintWriter out) {
        int[] ord=new int[h+w-1];
        fill(ord,Integer.MAX_VALUE);
        for(int i=0;i<h;i++)for(int j=0;j<w;j++){
            ord[i+j] = min(ord[i+j],order[i][j]);
        }
        String res = solve(ord,k);
        char[][] cs=new char[h][w];
        for(int i=0;i<h;i++)for(int j=0;j<w;j++)cs[i][j] = res.charAt(i+j);
        for(int i=0;i<h;i++){
            out.println(new String(cs[i]));
        }
    }
    private String solve(int[] ord, long k) {
        int n = ord.length;
        char[] res = new char[n];
        long[] ls=new long[n];
        for(int i=0;i<n;i++){
            ls[i] = ((long)ord[i])<<32 | i;
        }
        sort(ls);
        for(int i=0;i<n;i++)ord[i] = (int)ls[i];
        for(int i=0;i<n;i++){
            res[ord[i]] = '(';
            long val = calc(res);
            if(val>=k){
            }else{
                k-=val;
                res[ord[i]] = ')';
            }
        }
        return new String(res);
    }
    String S="()";
    long INF = 1000000000000000100L;
    private long calc(char[] cs) {
        int n = cs.length;
        long[][] dp=new long[n+1][n+1];
        dp[0][0]=1;
        for(int i=0;i<n;i++)for(int j=0;j<n;j++)if(dp[i][j]>0){
            for(int k=0;k<2;k++)if(cs[i]==0 || cs[i]==S.charAt(k)){
                if(k==0){
                    dp[i+1][j+1] += dp[i][j];
                    if(dp[i+1][j+1]>INF)dp[i+1][j+1]=INF;
                }else{
                    if(j>0){
                        dp[i+1][j-1] += dp[i][j];
                        if(dp[i+1][j-1]>INF)dp[i+1][j-1]=INF;
                    }
                }
            }
        }
        return dp[n][0];
    }
    private String next(InputStream in) {
        try {
            StringBuilder res = new StringBuilder("");
            int c = in.read();
            while (Character.isWhitespace(c))
                c = in.read();
            do {
                res.append((char) c);
            } while (!Character.isWhitespace(c = in.read()));
            return res.toString();
        } catch (Exception e) {
            return null;
        }
    }

    private int nextInt(InputStream in){
        try{
            int c=in.read();
            if(c==-1) return c;
            while(c!='-'&&(c<'0'||'9'<c)){
                c=in.read();
                if(c==-1) return c;
            }
            if(c=='-') return -nextInt(in);
            int res=0;
            do{
                res*=10;
                res+=c-'0';
                c=in.read();
            }while('0'<=c&&c<='9');
            return res;
        }catch(Exception e){
            return -1;
        }
    }
    
    private long nextLong(InputStream in){
        try{
            int c=in.read();
            if(c==-1) return c;
            while(c!='-'&&(c<'0'||'9'<c)){
                c=in.read();
                if(c==-1) return c;
            }
            if(c=='-') return -nextLong(in);
            long res=0;
            do{
                res*=10;
                res+=c-'0';
                c=in.read();
            }while('0'<=c&&c<='9');
            return res;
        }catch(Exception e){
            return -1;
        }
    }
}