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;
inline void read(register int *n) {
  register char c;
  *n = 0;
  do {
    c = getchar();
  } while (c < '0' || c > '9');
  do {
    *n = c - '0' + *n * 10;
    c = getchar();
  } while (c >= '0' && c <= '9');
}
const long long INF = 2LL * 1000 * 1000 * 1000 * 1000 * 1000 * 1000;
long long dp[500][500 * 2];
string mask;
int n;
long long f(int pos, int bal) {
  if (pos == -1) return bal == 0 ? 1 : 0;
  if (bal < 0) return 0;
  if (bal < -n || bal > n) return 0;
  long long &res = dp[pos][bal];
  if (res != -1) return res;
  if (mask[pos] == ')')
    return res = f(pos - 1, bal + 1);
  else if (mask[pos] == '(')
    return res = f(pos - 1, bal - 1);
  else
    return res = min(INF, f(pos - 1, bal + 1) + f(pos - 1, bal - 1));
}
long long cnt() {
  memset(dp, -1, sizeof dp);
  n = ((int)(mask).size());
  return f(n - 1, 0);
}
int main(int argv, char **argc) {
  long long r, c, k;
  cin >> r >> c >> k;
  vector<pair<int, int> > V(r + c - 1);
  for (register int i = (0); i < (((int)(V).size())); ++i)
    V[i].second = i, V[i].first = 10000;
  for (register int i = (0); i < (r); ++i)
    for (register int j = (0); j < (c); ++j) {
      int p = i * c + j;
      cin >> p;
      V[i + j].first = min(p, V[i + j].first);
    }
  mask = string(((int)(V).size()), '?');
  sort((V).begin(), (V).end());
  for (int i = 0; i < ((int)(V).size()); i++) {
    mask[V[i].second] = '(';
    long long tot = cnt();
    if (tot < k || tot == 0) {
      k -= tot;
      mask[V[i].second] = ')';
    }
  }
  for (register int i = (0); i < (r); ++i) {
    for (register int j = (0); j < (c); ++j) cout << mask[i + j];
    cout << "\n";
  }
  return 0;
}
