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 double eps = 1e-8;
char ans[107][107];
unsigned long long f[207][107];
int res[207];
int n, m;
unsigned long long k;
vector<pair<int, pair<int, int> > > cor;
const unsigned long long infi = 1200000000000000000ull;
long long calc() {
  memset(f, 0, sizeof(f));
  f[0][1] = 1;
  for (int i = 1; i < n + m - 1; ++i)
    for (int j = 0; j <= min(i + 1, (n + m) / 2); ++j) {
      if (j) f[i][j] = f[i - 1][j - 1];
      if (res[i] == 0) f[i][j] += f[i - 1][j + 1];
      if (res[i] == -1) f[i][j] = f[i - 1][j + 1];
      if (f[i][j] > infi) f[i][j] = infi;
    }
  return f[n + m - 2][0];
}
int main() {
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      int c;
      cin >> c;
      cor.push_back(make_pair(c, make_pair(i, j)));
    }
  sort(cor.begin(), cor.end());
  memset(ans, 0, sizeof(ans));
  memset(res, 0, sizeof(res));
  for (int i = 0; i < n * m; i++)
    if (ans[cor[i].second.first][cor[i].second.second] == 0) {
      int x = cor[i].second.first, y = cor[i].second.second;
      res[x + y] = 1;
      long long step = calc();
      if (k > step) {
        k -= step;
        res[x + y] = -1;
      }
      for (int i = 0; i <= x + y; ++i)
        if (i < n && x + y - i < m)
          if (res[x + y] == 1)
            ans[i][x + y - i] = '(';
          else
            ans[i][x + y - i] = ')';
    }
  for (int i = 0; i < n; i++) cout << ans[i] << endl;
  return 0;
}
