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;
char ans[205][205], seq[205];
int in[205][205];
pair<int, int> pri[205];
unsigned long long dp[205][205];
unsigned long long count(int n) {
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j <= (n / 2); ++j) {
      if (j && seq[i - 1] != ')') dp[i][j] = dp[i - 1][j - 1];
      if (seq[i - 1] != '(') dp[i][j] += dp[i - 1][j + 1];
      dp[i][j] = min(1000000000000000001ull, dp[i][j]);
    }
  }
  return dp[n][0];
}
void go(int n, unsigned long long k) {
  for (int i = 0; i < n; ++i) {
    int idx = pri[i].second;
    seq[idx] = '(';
    unsigned long long temp = count(n);
    if (k >= temp) {
      k -= temp;
      seq[idx] = ')';
    }
  }
}
vector<pair<int, int> > get(int pos, int n, int m) {
  vector<pair<int, int> > ans;
  for (int i = 0; i < n && pos >= 0; ++i, --pos)
    if (pos < m) ans.push_back(make_pair(i, pos));
  return ans;
}
int main() {
  int n, m;
  unsigned long long k;
  cin >> n >> m >> k;
  int len = n + m - 1;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) cin >> in[i][j];
  for (int i = 0; i < len; ++i) {
    vector<pair<int, int> > aux = get(i, n, m);
    pri[i] = make_pair(in[aux[0].first][aux[0].second], i);
    for (int j = 1; j < aux.size(); ++j)
      pri[i] = min(pri[i], make_pair(in[aux[j].first][aux[j].second], i));
  }
  sort(pri, pri + len);
  go(len, k - 1);
  for (int i = 0; i < len; ++i) {
    vector<pair<int, int> > aux = get(i, n, m);
    for (int j = 0; j < aux.size(); ++j)
      ans[aux[j].first][aux[j].second] = seq[i];
  }
  for (int i = 0; i < n; ++i) cout << ans[i] << endl;
  return 0;
}
