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 N = 2e2 + 10;
long long n, m, k, mn[N], ans[N];
long double dp[N][N];
vector<pair<long long, long long> > vec;
void solve(long long indx) {
  memset(dp, 0, sizeof dp);
  ans[indx] = 1;
  dp[0][1] = 1;
  for (long long i = 1; i < n; i++)
    for (long long j = 0; j <= i + 1; j++) {
      if (ans[i] == 1)
        dp[i][j] = dp[i - 1][j - 1];
      else if (ans[i] == 2)
        dp[i][j] = dp[i - 1][j + 1];
      else {
        if (j)
          dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j + 1];
        else
          dp[i][j] = dp[i - 1][j + 1];
      }
    }
  if (dp[n - 1][0] < k) k -= dp[n - 1][0], ans[indx] = 2;
}
int32_t main() {
  memset(mn, 127, sizeof mn);
  cin >> n >> m >> k;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) {
      long long x;
      cin >> x;
      mn[i + j] = min(mn[i + j], x);
    }
  n += m - 1;
  for (long long i = 0; i < n; i++) vec.push_back({mn[i], i});
  sort(vec.begin(), vec.end());
  for (pair<long long, long long> p : vec) solve(p.second);
  n -= m - 1;
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++)
      if (ans[i + j] == 1)
        cout << '(';
      else
        cout << ')';
    cout << '\n';
  }
}
