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 MAXN = 1000000000000000001LL;
char ANS[201];
long long dp[201][201], ff;
pair<long, long> P[10001];
long n, m, i, j, k, l;
inline void add(long long &X, const long long Y) {
  X += Y;
  if (MAXN < X) X = MAXN;
}
inline bool check() {
  memset(dp, 0, sizeof(dp));
  dp[0][1] = 1;
  long ii, jj;
  for (ii = 1; ii <= n + m - 2; ++ii) {
    if (ANS[ii] != '(') {
      for (jj = 0; jj < l; ++jj) add(dp[ii][jj], dp[ii - 1][jj + 1]);
    }
    if (ANS[ii] != ')') {
      for (jj = 1; jj <= l; ++jj) add(dp[ii][jj], dp[ii - 1][jj - 1]);
    }
  }
  return dp[n + m - 2][0] < ff;
}
int main() {
  ANS[0] = '(';
  cin >> n >> m >> ff;
  for (i = 0; i < n; ++i)
    for (j = 0; j < m; ++j) cin >> k, P[k].first = i, P[k].second = j;
  ANS[n + m - 2] = ')', l = (n + m - 1) / 2;
  for (i = 1; i <= n * m; ++i)
    if (!ANS[P[i].first + P[i].second]) {
      ANS[P[i].first + P[i].second] = '(';
      if (check()) {
        ANS[P[i].first + P[i].second] = ')', ff -= dp[n + m - 2][0];
      }
    }
  for (i = 0; i < n; ++i) {
    for (j = 0; j < m; ++j) cout << ANS[i + j];
    cout << endl;
  }
  cin >> n;
  return 0;
}
