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 java.math.*;


public class e {
    BufferedReader in;
    StringTokenizer st;
    PrintWriter out;

    String _token() throws IOException {
        while (in.ready() && !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    int _int() throws NumberFormatException, IOException {
        return Integer.parseInt(_token());
    }

    long _long() throws NumberFormatException, IOException {
        return Long.parseLong(_token());
    }

    double _double() throws NumberFormatException, IOException {
        return Double.parseDouble(_token());
    }

    void deb(String s) {
        System.err.println(s);
    }

    void deb(Object a) {
        System.err.println(a.toString());
    }

    void init(boolean FILE, String name) throws NumberFormatException,
            IOException {
        Locale.setDefault(Locale.US);
        if (FILE) {
            in = new BufferedReader(new FileReader(name + ".in"));
            out = new PrintWriter(name + ".out");
        } else {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
        st = new StringTokenizer("");
    }

    int x[],y[],n,m;
    long k;
    int answer[];
    
    char ans[][];
    
    
    long count(int pos, int t) {
        long clc[][] = new long[n+m][n+m];
        clc[0][1] = 1;
        for(int i=1;i<n+m-1;i++) {
            for(int sum=0; sum<n+m; sum++) {
                int w;
                if (answer[i] != -1) {
                    w = 1-2*answer[i];
                    if (sum+w >= 0 && sum+w<n+m) {
                        clc[i][sum+w] += clc[i-1][sum]; 
                        if (clc[i][sum+w] >= Long.MAX_VALUE/2)
                            clc[i][sum+w] = Long.MAX_VALUE/2; 
                    }
                } else {
                    w = 1;
                    if (sum+w >= 0 && sum+w<n+m) {
                        clc[i][sum+w] += clc[i-1][sum]; 
                        if (clc[i][sum+w] >= Long.MAX_VALUE/2)
                            clc[i][sum+w] = Long.MAX_VALUE/2; 
                    }
                    
                    w = -1;
                    if (sum+w >= 0 && sum+w<n+m) {
                        clc[i][sum+w] += clc[i-1][sum]; 
                        if (clc[i][sum+w] >= Long.MAX_VALUE/2)
                            clc[i][sum+w] = Long.MAX_VALUE/2; 
                    }
                }
            }

        }
        
        
        return clc[n+m-2][0];   
    }
    
    void solve(int pos) {
        if (pos == n*m)
            return;
        if (answer[x[pos] + y[pos]] != -1) {
            ans[x[pos]][y[pos]] = (char)(answer[x[pos] + y[pos]]*')' + 
                                  (1 - answer[x[pos] + y[pos]])*'('); 
        } else {
            answer[x[pos] + y[pos]] = 0;
            long t = count(pos,0);
            ans[x[pos]][y[pos]] = '('; 
            if (t <= k) {
                answer[x[pos] + y[pos]] = 1;
                k-=t;
                ans[x[pos]][y[pos]] = ')'; 
            }
        }
        solve(pos+1);
    }
    void mainProgram() throws NumberFormatException, IOException {
        //      test("e.in");
        init(false, "e");
        
        n = _int();
        m = _int();
        k = _long() - 1;
        
        int p[][] = new int[n][m];
        answer = new int[n+m];
        Arrays.fill(answer, -1);
        
        x = new int[n*m];
        y = new int[n*m];
        for(int i=0;i<n;i++)
            for(int j=0;j<m;j++) {
                p[i][j] = _int() - 1;
                x[p[i][j]] = i;
                y[p[i][j]] = j;
            }
        
        ans = new char[n][m];
        solve(0);
        
        for(int i=0;i<n;i++)
            out.println(new String(ans[i]));
            
        out.close();
    }

    int rand(int x) {
        return (int) (Math.random() * x);
    }

    void test(String name) throws IOException {
        out = new PrintWriter(new File(name));

        out.close();
    }

    public static void main(String[] args) throws NumberFormatException,
            IOException {
        long T = System.currentTimeMillis();
        new e().mainProgram();
        System.err.println("Time of working: "
                + (System.currentTimeMillis() - T) + " ms");
    }

    BigInteger add(BigInteger A, BigInteger B) {
        return A.add(B);
    }

    BigInteger mult(BigInteger A, BigInteger B) {
        return A.multiply(B);
    }

    BigInteger sub(BigInteger A, BigInteger B) {
        return A.subtract(B);
    }

    BigInteger div(BigInteger A, BigInteger B) {
        return A.divide(B);
    }

    BigInteger mi(BigInteger A) {
        return (BigInteger.ZERO).subtract(A);
    }

    BigInteger sq(BigInteger A) {
        return A.multiply(A);
    }

    BigInteger val(long a) {
        return BigInteger.valueOf(a);
    }

    int cmp(BigInteger a, BigInteger b) {
        return a.compareTo(b);
    }

}
