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;
const int maxsize = 200;
char s[maxsize];
int mp[maxsize];
int p[maxsize][maxsize];
long long a[maxsize];
int n, m;
long long k;
long long dp[210][210];
long long sum(long long a, long long b) {
  return a + b > 1000000000000000001LL ? 1000000000000000001LL : a + b;
}
int main() {
  memset(s, 0, sizeof s);
  cin >> n >> m >> k;
  int kk = n + m - 1;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) cin >> p[i][j];
  for (int i = 0; i < kk; ++i) {
    int MIN = 1000000000;
    for (int j = 0; i - j >= 0; ++j)
      if (i - j < n && j < m) MIN = min(MIN, p[i - j][j]);
    mp[i] = MIN;
  }
  s[0] = '(';
  s[kk - 1] = ')';
  mp[0] = 1000000000;
  mp[kk - 1] = 1000000000;
  for (int ii = 2; ii < kk; ++ii) {
    int minpos = 0;
    for (int i = 0; i < kk; ++i)
      if (mp[i] < mp[minpos]) minpos = i;
    s[minpos] = '(';
    {
      memset(dp, 0, sizeof dp);
      dp[0][0] = 1;
      for (int i = 0; i < kk; ++i)
        for (int j = 0; j <= i && i + j <= kk; ++j) {
          if (s[i] == '(')
            dp[i + 1][j + 1] = sum(dp[i + 1][j + 1], dp[i][j]);
          else if (s[i] == ')')
            dp[i + 1][j - 1] = sum(dp[i + 1][j - 1], dp[i][j]);
          else {
            dp[i + 1][j - 1] = sum(dp[i + 1][j - 1], dp[i][j]);
            dp[i + 1][j + 1] = sum(dp[i + 1][j + 1], dp[i][j]);
          }
        }
    }
    if (k > dp[kk][0]) {
      k -= dp[kk][0];
      s[minpos] = ')';
    }
    mp[minpos] = 1000000000;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) cout << s[i + j];
    cout << endl;
  }
  return 0;
}
