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.
//package round92;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;

public class C {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), m = ni();
		long k = nl();
		
		int[][] pr = new int[n][m];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				pr[i][j] = ni();
			}
		}
		
		int[][] dpr = new int[n+m-1][2];
		for(int i = 0;i < n+m-1;i++){
			dpr[i][0] = 999999;
		}
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				dpr[i+j][0] = Math.min(dpr[i+j][0], pr[i][j]);
				dpr[i+j][1] = i+j;
			}
		}
		
		Arrays.sort(dpr, new Comparator<int[]>(){
			public int compare(int[] a, int[] b){
				return a[0] - b[0];
			}
		});
		
		k--;
		char[] str = new char[n+m-1];
		Arrays.fill(str, '.');
		for(int i = 0;i < n+m-1;i++){
			str[dpr[i][1]] = '(';
			long c = count(str);
//			tr(i, dpr[i][1], k, c);
			if(k < c){
			}else{
				k -= c;
				str[dpr[i][1]] = ')';
			}
		}
		if(k != 0)throw new AssertionError(k);
		
		for(int i = 0;i < n;i++){
			char[] ret = new char[m];
			for(int j = 0;j < m;j++){
				ret[j] = str[i+j];
			}
			out.println(new String(ret));
		}
	}
	
	long count(char[] str)
	{
		int n = str.length;
		if(n % 2 == 1)return 0;
		long[][] dp = new long[n+1][n+1];
		dp[0][0] = 1;
		long INF = 1000000000000000005L;
		for(int i = 1;i <= n;i++){
			if(str[i-1] == '.'){
				for(int j = 0;j <= n;j++){
					if(j-1 >= 0)dp[i][j] += dp[i-1][j-1];
					if(j+1 <= n)dp[i][j] += dp[i-1][j+1];
					if(dp[i][j] > INF)dp[i][j] = INF;
				}
			}else if(str[i-1] == '('){
				for(int j = 0;j <= n;j++){
					if(j-1 >= 0)dp[i][j] += dp[i-1][j-1];
					if(dp[i][j] > INF)dp[i][j] = INF;
				}
			}else{
				for(int j = 0;j <= n;j++){
					if(j+1 <= n)dp[i][j] += dp[i-1][j+1];
					if(dp[i][j] > INF)dp[i][j] = INF;
				}
			}
		}
		return dp[n][0];
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception
	{
		new C().run();
	}
	
	public int ni()
	{
		try {
			int num = 0;
			boolean minus = false;
			while((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'));
			if(num == '-'){
				num = 0;
				minus = true;
			}else{
				num -= '0';
			}
			
			while(true){
				int b = is.read();
				if(b >= '0' && b <= '9'){
					num = num * 10 + (b - '0');
				}else{
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}
	
	public long nl()
	{
		try {
			long num = 0;
			boolean minus = false;
			while((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'));
			if(num == '-'){
				num = 0;
				minus = true;
			}else{
				num -= '0';
			}
			
			while(true){
				int b = is.read();
				if(b >= '0' && b <= '9'){
					num = num * 10 + (b - '0');
				}else{
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}
	
	public String ns()
	{
		try{
			int b = 0;
			StringBuilder sb = new StringBuilder();
			while((b = is.read()) != -1 && (b == '\r' || b == '\n' || b == ' '));
			if(b == -1)return "";
			sb.append((char)b);
			while(true){
				b = is.read();
				if(b == -1)return sb.toString();
				if(b == '\r' || b == '\n' || b == ' ')return sb.toString();
				sb.append((char)b);
			}
		} catch (IOException e) {
		}
		return "";
	}
	
	public char[] ns(int n)
	{
		char[] buf = new char[n];
		try{
			int b = 0, p = 0;
			while((b = is.read()) != -1 && (b == ' ' || b == '\r' || b == '\n'));
			if(b == -1)return null;
			buf[p++] = (char)b;
			while(p < n){
				b = is.read();
				if(b == -1 || b == ' ' || b == '\r' || b == '\n')break;
				buf[p++] = (char)b;
			}
			return Arrays.copyOf(buf, p);
		} catch (IOException e) {
		}
		return null;
	}
	
	
	double nd() { return Double.parseDouble(ns()); }
	boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
