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 = 200 + 10, INF = 1e18;
long long dp[N][N], a[N][N], val[N], tmp[N], fix[N];
long long n, m, k;
inline long long solve() {
  memset(dp, 0, sizeof dp);
  dp[0][1] = 1;
  for (long long i = 1; i < n + m - 1; i++)
    for (long long j = 0; j <= i + 1; j++) {
      if (fix[i] == 1 && j)
        dp[i][j] = dp[i - 1][j - 1];
      else if (fix[i] == 2)
        dp[i][j] = dp[i - 1][j + 1];
      else if (fix[i] == 0)
        dp[i][j] = min((j ? dp[i - 1][j - 1] : 0) + dp[i - 1][j + 1], INF);
    }
  return dp[n + m - 2][0];
}
int32_t main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  fill(val, val + N, INF);
  cin >> n >> m >> k;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) cin >> a[i][j];
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) val[i + j] = min(val[i + j], a[i][j]);
  for (long long i = 0; i < n + m - 1; i++) tmp[i] = i;
  sort(tmp, tmp + n + m - 1,
       [&](long long i, long long j) { return val[i] < val[j]; });
  for (long long i = 0; i < n + m - 1; i++) {
    long long x = tmp[i];
    fix[x] = 1;
    long long cnt = solve();
    if (cnt < k) {
      fix[x] = 2;
      k -= cnt;
    }
  }
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) cout << (fix[i + j] == 1 ? '(' : ')');
    cout << '\n';
  }
}
