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.util.*;
import java.io.*;
public class E {
	static long[][] dp;
    public static void main(String[] args) throws IOException {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt(), m = s.nextInt();
        long k = s.nextLong();
        int[][] pr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                pr[i][j]=s.nextInt();
            }
        }
        int max = n+m-1;
        int[] priority = new int[max];
        for (int i = 0; i < max; i++) {
            for (int x = 0 ; x < max; x++) {
                if (x < n && i-x >= 0 && i-x < m) {
                    int blah = pr[x][i-x];
                    if (priority[i]==0) {
                        priority[i] = blah;
                    } else {
                        priority[i] = Math.min(priority[i], blah);
                    }
                }
            }
        }
        List<Pair> list = new ArrayList<Pair>();
        for (int i = 0; i < max; i++) {
            list.add(new Pair(priority[i], i));
        }
        Collections.sort(list);
        
        char[] ch = new char[max];
        int q = 0;
        for (Pair p : list) {
            ch[p.y] = '(';
            long ct = count(ch);
           //System.out.println(new String(ch));
//           System.out.println((q++)+":"+k+","+ct);
            if (k > ct) {
                ch[p.y] = ')';
                k -= ct;
            }
            //System.out.println(new String(ch));
        }
        char[][] ans = new char[n][m];
        for (int i = 0; i < max; i++) {
            for (int x = 0 ; x < max; x++) {
                if (x < n && i-x >= 0 && i-x < m) {
                    ans[x][i-x] = ch[i];
                }
            }
        }
        for (int i = 0; i < n; i++) {
           System.out.println(new String(ans[i]));
        }
    }
    public static class Pair implements Comparable<Pair> {
        int x, y;
        Pair(int x, int y) { this.x = x; this.y = y; }
        public int compareTo(Pair p) {
            if (x < p.x) return -1;
            else if (x > p.x) return 1;
            else return 0;
        }
        public String toString() { return "("+x+","+y+")"; }
    }
    public static long count(char[] existing){
        int n = existing.length;
        dp = new long[n+1][n+1];
        for (int i = 0; i <= n; i++) dp[0][i] = 0;
        dp[0][0] = 1;
        for (int upto = 1; upto <= n; upto++) {
        	for (int i = 0; i <= n; i++) {
        		long leftParen = (i-1 >= 0) ? dp[upto-1][i-1] : 0;
        		long rightParen = (i+1 <= n) ? dp[upto-1][i+1] : 0;
        		long sum = 0;
        		if (existing[upto-1] == '(') sum = leftParen;
        		else if (existing[upto-1] == ')') sum = rightParen;
        		else sum = safeAdd(leftParen, rightParen);
        		dp[upto][i] = sum;
        	}
        }
        return dp[n][0];
    }
    public static long INF = 4000000000000000000L;
    public static long safeAdd(long a, long b) {
        if (a+b > INF) return INF;
        else return a+b;
    }
}