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 C
{
	static int N, n2;
	static char[] X;
	
	static long[][] d;
	
	static long k;
	
	public static void init()
	{
		d = new long[N+1][];
		n2 = N/2;
		for (int i=1; i<=N;i++)
		{
			d[i] = new long[n2+3];
			d[i][0] = 0;
			d[i][n2+2] = 0;
		}
		
		for (int i=1; i<n2+2; i++)
		{
			d[1][i] = 0;
		}
		
		d[1][2] = 1;
	}
	
	public static long comb()
	{
		int i,j;
		for (i=2; i<=N; i++)
		{
			for (j=1;j<=n2+1;j++)
			{
				switch (X[i])
				{
					case '(':
						d[i][j] = d[i-1][j-1];
						break;
					case ')':
						d[i][j] = d[i-1][j+1];
						break;
					default:
						d[i][j] = d[i-1][j+1] + d[i-1][j-1];
				}
				
				if (d[i][j] > k)
				{
					d[i][j] = k;
				}
			}
		}
		return d[N][1];
	}

	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int m = in.nextInt();
		k = in.nextLong();
		
		N = n+m-1;
		
		int[] dg = new int[n*m+1];
		
		int i,j,x;
		
		for (i=1; i<=n; i++)
		{
			for (j=1; j<=m; j++)
			{
				x = in.nextInt();				
				dg[x] = i+j-1;
			}
		}
		
		X = new char[N+1];
		
		X[1] = '(';
		X[N] = ')';
		for (i=2;i<N;i++)
		{
			X[i] = '*';
		}
		
		init();
		
		int p=1;
		while ((p<=n*m)&&((dg[p]==1)||(dg[p]==N))  )
		{
			p++;
		}
		
		long c = 0;
		while (p<=n*m)
		{
			if (X[dg[p]]=='*')
			{
				X[dg[p]] = '(';
				c = comb();
				
				if (c<k)
				{
					X[dg[p]] = ')';
					k-= c;
				}
			}
			
			p++;
		}
		
		for (i=1; i<=n; i++)
		{
			for (j=1; j<=m; j++)
			{
				System.out.print(X[i+j-1]);
			}
			System.out.println();
		}
		
	}
}