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 C implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	final int NONE = -1, OPEN = 0, CLOSE = 1;

	private void solve() throws IOException {
		int height = nextInt(), width = nextInt(), total = height + width - 1;
		long k = nextLong();
		int[] priorities = new int[total];
		Arrays.fill(priorities, Integer.MAX_VALUE);
		for (int i = 0; i < height; i++) {
			for (int j = 0; j < width; j++) {
				int id = i + j, p = nextInt();
				priorities[id] = Math.min(priorities[id], p);
			}
		}
		int[] prioritiesSorted = Arrays.copyOf(priorities, total);
		Arrays.sort(prioritiesSorted);
		for (int i = 0; i < total; i++) {
			priorities[i] = Arrays
					.binarySearch(prioritiesSorted, priorities[i]);
		}
		int[] priorityToId = new int[total];
		for (int i = 0; i < total; i++) {
			priorityToId[priorities[i]] = i;
		}
		int[] already = new int[total];
		Arrays.fill(already, NONE);
		for (int i = 0; i < total; i++) {
			int id = priorityToId[i];
			already[id] = OPEN;
			long current = getWays(total, already);
			if (current < k) {
				k -= current;
				already[id] = CLOSE;
			}
		}
		if (k != 1) {
			throw new AssertionError();
		}
		char[][] result = new char[height][width];
		for (int i = 0; i < height; i++) {
			for (int j = 0; j < width; j++) {
				if (already[i + j] == OPEN) {
					result[i][j] = '(';
				} else if (already[i + j] == CLOSE) {
					result[i][j] = ')';
				} else {
					throw new AssertionError();
				}
			}
		}
		for (int i = 0; i < height; i++) {
			out.println(new String(result[i]));
		}
	}

	private long getWays(int n, int[] was) {
		BigInteger[][] d = new BigInteger[n + 1][n + 1];
		d[0][0] = BigInteger.ONE;
		for (int i = 0; i < n; i++) {
			for (int balance = 0; balance <= i; balance++) {
				if (d[i][balance] != null) {
					if (was[i] == OPEN) {
						if (balance + 1 <= n)
							d[i + 1][balance + 1] = add(d[i + 1][balance + 1],
									d[i][balance]);
					} else if (was[i] == CLOSE) {
						if (balance - 1 >= 0)
							d[i + 1][balance - 1] = add(d[i + 1][balance - 1],
									d[i][balance]);
					} else {
						if (balance + 1 <= n)
							d[i + 1][balance + 1] = add(d[i + 1][balance + 1],
									d[i][balance]);
						if (balance - 1 >= 0)
							d[i + 1][balance - 1] = add(d[i + 1][balance - 1],
									d[i][balance]);
					}
				}
			}
		}
		BigInteger result = d[n][0];
		if (result == null)
			return 0;
		else if (result.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0)
			return Long.MAX_VALUE;
		else
			return result.longValue();
	}

	private BigInteger add(BigInteger a, BigInteger b) {
		return (a == null) ? b : a.add(b);
	}

	public static void main(String[] args) {
		// final boolean oldChecker = false;
		//
		// if (oldChecker)
		// new Thread(null, new Template(), "yarrr", 1 << 24).start();
		// else
		new C().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}