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 long long INF = (long long)1000000 * 1000000 * 1500000, MAXN = 101;
struct brak {
  bool mark = false;
  bool what;
} Br[MAXN * 2];
long long n, m, k, x;
long long solve() {
  long long dp[x + 1][x + 1];
  memset(dp, 0, sizeof dp);
  dp[0][0] = 1;
  for (int i = 1; i <= x; i++)
    if (!Br[i - 1].mark)
      for (int l = i - i / 2; l <= i; l++)
        dp[l][i] = min(dp[l][i - 1] + dp[l - 1][i - 1], INF);
    else if (Br[i - 1].what == true)
      for (int l = i - i / 2; l <= i; l++) dp[l][i] = dp[l - 1][i - 1];
    else
      for (int l = i - i / 2; l <= i; l++) dp[l][i] = dp[l][i - 1];
  return dp[x / 2][x];
}
int main() {
  cin >> n >> m >> k;
  x = n + m - 1;
  long long pr[x];
  for (long long i = 0; i < x; i++) {
    pr[i] = INF;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      long long a;
      cin >> a;
      pr[i + j] = min(pr[i + j], (long long)a);
    }
  }
  vector<pair<long long, long long>> vec;
  for (long long i = 0; i < x; i++) {
    vec.push_back({pr[i], i});
  }
  sort(vec.begin(), vec.end());
  for (int i = 0; i < x; i++) {
    long long l = vec[i].second;
    Br[l].mark = 1;
    Br[l].what = 1;
    long long ans = solve();
    if (ans < k) {
      k -= ans;
      Br[l].what = 0;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << (char)('(' + !Br[i + j].what);
    }
    cout << endl;
  }
}
