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.
// practice with rainboy
import java.io.*;
import java.util.*;

public class CF123C extends PrintWriter {
	CF123C() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF123C o = new CF123C(); o.main(); o.flush();
	}

	static final long INF = 1000000000000000000L;
	byte[] cc; int n_;
	long[] dp, dq;
	long solve() {
		Arrays.fill(dp, 0); dp[0] = 1;
		for (int i = 0; i < n_; i++)
			if (cc[i] == '(') {
				for (int d = n_; d > 0; d--)
					dp[d] = dp[d - 1];
				dp[0] = 0;
			} else if (cc[i] == ')') {
				for (int d = 0; d < n_; d++)
					dp[d] = dp[d + 1];
				dp[n_] = 0;
			} else {
				dq[0] = dp[1];
				for (int d = 1; d < n_; d++)
					dq[d] = Math.min(dp[d - 1] + dp[d + 1], INF);
				dq[n_] = dp[n_ - 1];
				long[] tmp = dp; dp = dq; dq = tmp;
			}
		return dp[0];
	}
	void main() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		long k = sc.nextLong();
		n_ = n + m - 1;
		int[] pp = new int[n_];
		Arrays.fill(pp, n * m + 1);
		for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++) {
				int p = sc.nextInt();
				pp[i + j] = Math.min(pp[i + j], p);
			}
		Integer[] ii = new Integer[n_];
		for (int i = 0; i < n_; i++)
			ii[i] = i;
		Arrays.sort(ii, (i, j) -> pp[i] - pp[j]);
		cc = new byte[n_];
		dp = new long[n_ + 1];
		dq = new long[n_ + 1];
		for (int i = 0; i < n_; i++) {
			int i_ = ii[i];
			cc[i_] = '(';
			long k_;
			if ((k_ = solve()) < k) {
				k -= k_;
				cc[i_] = ')';
			}
		}
		byte[] aa = new byte[m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++)
				aa[j] = cc[i + j];
			println(new String(aa));
		}
	}
}
