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
{
	public static void main(String[] args) throws IOException
	{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

		StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
		int n = Integer.parseInt(tokenizer.nextToken());
		int m = Integer.parseInt(tokenizer.nextToken());
		long k = Long.parseLong(tokenizer.nextToken()) - 1;

		int [][] c = new int[n][m];
		for(int i = 0 ; i < n ; i++)
		{
			tokenizer = new StringTokenizer(reader.readLine());
			for(int j = 0 ; j < m ; j++)
				c[i][j] = Integer.parseInt(tokenizer.nextToken());
		}

		int [] order = new int[n+m-1];
		for(int i = 0 ; i < order.length ; i++)
		{
			int minX = 0, minY = 0;
			int minVal = n*m + 13;
			for(int j = 0 ; j < order.length ; j++)
			{
				int x, y;
				if(j < m)
				{
					x = 0;
					y = j;
				}
				else
				{
					x = j-m+1;
					y = m-1;
				}

				int v1 = x;
				int v2 = y;
				while(v1 < n && v2 >= 0)
				{
					if(c[v1][v2] < minVal)
					{
						minVal = c[v1][v2];
						minX = x;
						minY = y;
					}
					v1++;
					v2--;
				}
			}

			order[i] = minX+minY;
			int v1 = minX;
			int v2 = minY;
			while(v1 < n && v2 >= 0)
			{
				c[v1][v2] = n*m+13;
				v1++;
				v2--;
			}
		}


		char [] build = new char[n+m-1];
		Arrays.fill(build, '?');
		for(int o : order)
		{
			build[o] = '(';
			long calc = dynamic(build);
			if(k >= calc && calc != -1)
			{
				build[o] = ')';
				k -= calc;
			}
		}

		char [][] res = new char[n][m];
		for(int i = 0 ; i < n+m-1 ; i++)
		{
			int x, y;
			if(i < m)
			{
				x = 0;
				y = i;
			}
			else
			{
				x = i-m+1;
				y = m-1;
			}
			res[x][y] = build[i];
		}

		for(int i = 1 ; i < n ; i++)
			for(int j = 0 ; j < m-1 ; j++)
				res[i][j] = res[i-1][j+1];

		for(int i = 0 ; i < n ; i++)
			writer.println(new String(res[i]));

		writer.flush();
		writer.close();
	}

	private static long dynamic(char[] build)
	{
		int n = build.length;
		long [][] dp = new long[n+1][n+1];
		double [][] _dp = new double[n+1][n+1];
		dp[0][0] = 1;
		_dp[0][0] = 1;
		for(int i = 0 ; i < n ; i++)
			for(int open = 0 ; open <= n ; open++)
				if(_dp[i][open] > 0)
				{
					if(build[i] == '(' || build[i] == '?')
					{
						dp[i+1][open+1] += dp[i][open];
						_dp[i+1][open+1] += _dp[i][open];
					}
					if(open > 0 && (build[i] == ')' || build[i] == '?'))
					{
						dp[i+1][open-1] += dp[i][open];
						_dp[i+1][open-1] += _dp[i][open];
					}
				}

		if(_dp[n][0] > 1.5e18)
			dp[n][0] = -1;
		return dp[n][0];
	}
}