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 unsigned long long N = 206;
unsigned long long n, m, k, c[N], s, INF = 1e18 + 1;
unsigned long long dp[N][N];
int p[N];
pair<unsigned long long, unsigned long long> q[N];
int main() {
  ios::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  for (int i = 0; i < N; i++) c[i] = 1e18;
  cin >> n >> m >> k;
  s = m + n - 1;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      unsigned long long x;
      cin >> x;
      c[i + j] = min(c[i + j], x);
    }
  for (int i = 0; i < s; i++) q[i].first = c[i], q[i].second = i;
  sort(q, q + s);
  for (int i = 0; i < s; i++) {
    p[q[i].second] = 1;
    if (p[0] != 2)
      dp[0][1] = 1;
    else
      dp[0][1] = 0;
    for (int j = 1; j < s; j++) {
      for (int u = 0; u <= j + 1 and u <= s - 1 - j; u++) {
        dp[j][u] = 0;
        if (p[j] == 1) {
          if (u) dp[j][u] = dp[j - 1][u - 1];
        } else if (p[j] == 2) {
          if (u + 1 <= j and u + 1 <= s - j) dp[j][u] = dp[j - 1][u + 1];
        } else {
          if (u) dp[j][u] = dp[j - 1][u - 1];
          if (u + 1 <= j and u + 1 <= s - j) dp[j][u] += dp[j - 1][u + 1];
        }
        dp[j][u] = min(dp[j][u], INF);
      }
    }
    if (dp[s - 1][0] < k or dp[s - 1][0] == 0) {
      p[q[i].second] = 2;
      k -= dp[s - 1][0];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++)
      if (p[i + j] == 1)
        cout << "(";
      else
        cout << ")";
    cout << endl;
  }
}
