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;
signed long long k;
const signed long long INF = 1000000000000000000 + 50;
signed long long Licz(string nap) {
  int n = nap.size();
  vector<vector<signed long long> > dp(n + 1,
                                       vector<signed long long>(n + 1, 0));
  if (nap[0] == '?' || nap[0] == '(') dp[1][1] = 1;
  for (int i = 1; i < n; ++i) {
    for (int otw = 1; otw <= n; ++otw) {
      int zam = i - otw;
      if (nap[i] == '?') {
        if (otw + 1 >= zam) dp[i + 1][otw + 1] += dp[i][otw];
        if (otw >= zam + 1) dp[i + 1][otw] += dp[i][otw];
      }
      if (nap[i] == '(')
        if (otw + 1 >= zam) dp[i + 1][otw + 1] += dp[i][otw];
      if (nap[i] == ')')
        if (otw >= zam + 1) dp[i + 1][otw] += dp[i][otw];
      if (dp[i + 1][otw] >= INF) dp[i + 1][otw] = INF;
      if (dp[i + 1][otw + 1] >= INF) dp[i + 1][otw + 1] = INF;
    }
  }
  return dp[n][n / 2];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> m >> k;
  vector<int> prio(n * m);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      int p;
      cin >> p;
      --p;
      prio[p] = i + j;
    }
  }
  string odp(n + m - 1, '?');
  for (int i = 0; i < n * m; ++i) {
    if (odp[prio[i]] == '?') {
      odp[prio[i]] = '(';
      signed long long ile = Licz(odp);
      if (ile < k) {
        odp[prio[i]] = ')';
        k -= ile;
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) cout << odp[i + j];
    cout << endl;
  }
  return 0;
}
