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.*;

public class E {
    static int n, m, nn;
    static long k;
    static int[] order;
    static long[][] c;
    static int[] paren;
    static final long inf = (1L << 63)-1;

    static void insertionsort(int[] a, int[] pri, int n) { 
	int i,j,v; 
	for (i=1; i<n; i++) { 
	    v = a[i]; 
	    for (j=i-1; j>=0; j--) { 
		if (pri[v] >= pri[a[j]]) break; 
		a[j+1] = a[j]; 
	    } 
	    a[j+1] = v; 
	} 
    }

    static long add(long a, long b) {
	if (a+b<0) return inf; else return a+b;
    }
    static long mult(long a, long b) {
	if (a==0L || b==0L) return 0L;
	if (a*b/b == a) return a*b; else return inf;
    }

    static long count_c1(int i, int j) {
	if (i>j-1 || paren[i]==2 || paren[j]==1 || (j-i)%2==0) return 0;
	if (i==j-1) return 1;
	return count_c(i+1, j-1);
    }

    static long count_c(int i, int j) {
	if (i>j-1 || paren[i]==2 || paren[j]==1 || (j-i)%2==0) return 0;
	if (i==j-1) return 1;
	if (c[i][j] >= 0) return c[i][j];
	long total = count_c(i+1,j-1);
	for(int k=i+1; k<j-1; k++) {
	    //	    total += count_c1(i,k) * count_c(k+1,j);
	    total = add(total, mult(count_c1(i,k),count_c(k+1,j)));
	    if (total==inf) break;
	}
	c[i][j] = total;
	return total;
    }

    public static void main(String[] args) throws Exception {
	Scanner sc = new Scanner(System.in);
	n = sc.nextInt();
	m = sc.nextInt();
	k = sc.nextLong()-1;  // use 0 based indexing
	nn = n+m-1;
	int[] pri = new int[nn];
	for (int i=0; i<nn; i++) pri[i] = n*m+1;
	for (int i=0; i<n; i++) {
	    for (int j=0; j<m; j++) {
		int z = sc.nextInt();
		if (pri[i+j] > z) pri[i+j] = z;
	    }
	}

	order = new int[nn];
	for (int i=0; i<nn; i++) order[i] = i;
	insertionsort(order, pri, nn);

	/*
	for (int i=0; i<nn; i++) {
	    System.out.printf("order[%d] = %d\n", i, order[i]);
	}
	*/

	c = new long[nn][nn];
	for (int i=0; i<nn; i++) for (int j=0; j<nn; j++) c[i][j] = -1;
	paren = new int[nn];  // 0=unspecified, 1='(', 2=')'

	//	System.out.printf("count_c(%d,%d) = %d\n", 0, nn-1,count_c(0,nn-1));
	
	for (int ii=0; ii<nn; ii++) {
	    paren[order[ii]] = 1;
	    for (int i=0; i<=order[ii]; i++) for (int j=order[ii]; j<nn; j++) c[i][j] = -1;
	    long count = count_c(0,nn-1);
	    if (count <= k) {
		k = k-count;
		paren[order[ii]] = 2;
		for (int i=0; i<=order[ii]; i++) for (int j=order[ii]; j<nn; j++) c[i][j] = -1;
	    }
	}

	for (int i=0; i<n; i++) {
	    for (int j=0; j<m; j++) {
		System.out.print((paren[i+j]==1)?'(':')');
	    }
	    System.out.println();
	}

	/*	
	for (int i=0; i<nn; i++) {
	    System.out.printf("%c", (paren[i]==1)?'(':')');
	}
	System.out.println();
	*/
    }
}
