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.
#include <bits/stdc++.h>
using namespace std;
int n, m;
long long k;
int p[105][105];
int pp[10005];
int u[205];
vector<int> o;
char s[205];
long long calc(int L, int R) {
  long long dp[205] = {};
  dp[0] = 1;
  for (int i = L; i <= R; i++) {
    long long nxt[205] = {};
    if (s[i] == '(') {
      for (int j = i - L + 1; j > 0; j--) dp[j] = dp[j - 1];
      dp[0] = 0;
    } else if (s[i] == ')') {
      for (int j = 0; j < i - L + 1; j++) dp[j] = dp[j + 1];
      dp[i - L + 1] = 0;
    } else {
      for (int j = 0; j <= i - L + 1; j++)
        nxt[j] = min(1LL << 61,
                     (j ? dp[j - 1] : 0) + (j < i - L + 1 ? dp[j + 1] : 0));
      for (int j = 0; j <= i - L + 1; j++) dp[j] = nxt[j];
    }
  }
  return dp[0];
}
int main(void) {
  scanf("%d%d%I64d", &n, &m, &k);
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= m; j++) {
      scanf("%d", &p[i][j]);
      pp[p[i][j]] = i + j;
    }
  for (int i = 1; i <= n * m; i++)
    if (u[pp[i]] == 0) {
      o.push_back(pp[i]);
      u[pp[i]] = 1;
    }
  for (int i = 0; i < n + m - 1; i++) {
    int pos = o[i];
    s[pos] = '(';
    long long v = calc(2, n + m);
    if (v < k) {
      k -= v;
      s[pos] = ')';
    }
  }
  for (int i = 1; i <= n; i++, puts(""))
    for (int j = 1; j <= m; j++) printf("%c", s[i + j]);
  return 0;
}
