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 int maxN = 110;
int n, m;
long long k;
int p[maxN << 1];
const long long INF = 1.1e18;
int arr[maxN << 1];
const int O = 150;
bool vis[maxN << 1][maxN << 2];
long long memo[maxN << 1][maxN << 2];
long long dp(int pos, int sum) {
  if (sum < 0) return 0;
  if (pos == n + m - 1) return sum == 0;
  if (vis[pos][sum]) return memo[pos][sum];
  long long &ans = memo[pos][sum] = 0;
  if (arr[pos])
    ans = dp(pos + 1, sum + arr[pos]);
  else {
    ans += dp(pos + 1, sum + 1);
    ans += dp(pos + 1, sum - 1);
    ans = min(ans, INF);
  }
  vis[pos][sum] = 1;
  return ans;
}
int main() {
  cin >> n >> m >> k;
  memset(p, 1, sizeof p);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      int x;
      cin >> x;
      p[i + j] = min(p[i + j], x);
    }
  }
  vector<pair<int, int>> o;
  for (int i = 0; i < n + m - 1; ++i) {
    o.push_back({p[i], i});
  }
  sort(begin(o), end(o));
  for (auto e : o) {
    arr[e.second] = 1;
    memset(vis, 0, sizeof vis);
    long long cnt = dp(0, 0);
    if (cnt < k) arr[e.second] = -1, k -= cnt;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      cout << (arr[i + j] == 1 ? '(' : ')');
    }
    cout << endl;
  }
  return 0;
}
