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 MN = 211;
long long m, n, k;
long long p[MN][MN], priority[MN];
pair<long long, long long> order[MN];
char res[MN];
long long f[MN][MN];
const long long INF = 1000111000111000111LL;
long long solve() {
  memset(f, 0, sizeof f);
  f[0][0] = 1;
  for (long long i = (0), _b = (n - 1); i <= _b; ++i)
    for (long long s = (0), _b = (i); s <= _b; ++s) {
      long long t = f[i][s];
      if (!t) continue;
      if (t > INF) t = f[i][s] = INF;
      if (res[i + 1] == '(') {
        f[i + 1][s + 1] += t;
      } else if (res[i + 1] == ')') {
        if (s) {
          f[i + 1][s - 1] += t;
        }
      } else {
        f[i + 1][s + 1] += t;
        if (s) f[i + 1][s - 1] += t;
      }
    }
  return f[n][0];
}
int main() {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cout << (fixed) << setprecision(9);
  while (cin >> m >> n >> k) {
    long long savem = m, saven = n;
    for (long long i = (1), _b = (m + n - 1); i <= _b; ++i)
      priority[i] = MN * MN;
    for (long long i = (1), _b = (m); i <= _b; ++i)
      for (long long j = (1), _b = (n); j <= _b; ++j) {
        cin >> p[i][j];
        long long s = i + j - 1;
        priority[s] = min(priority[s], p[i][j]);
      }
    n = m + n - 1;
    for (long long i = (1), _b = (n); i <= _b; ++i)
      order[i] = make_pair(priority[i], i);
    sort(order + 1, order + n + 1);
    memset(res, 0, sizeof res);
    for (long long i = (1), _b = (n); i <= _b; ++i) {
      long long pos = order[i].second;
      res[pos] = '(';
      long long cur = solve();
      if (cur >= k) continue;
      res[pos] = ')';
      k -= cur;
    }
    for (long long i = (1), _b = (savem); i <= _b; ++i) {
      for (long long j = (1), _b = (saven); j <= _b; ++j)
        cout << res[i + j - 1];
      cout << '\n';
    }
  }
}
