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;
template <class T>
T sqr(const T &a) {
  return a * a;
}
int result[300];
long long dp[300][300];
const long long MAX = 1e18 + 100;
long long f(int n) {
  for (int i = 0; i < (n + 1); i++)
    for (int j = 0; j < (n + 1); j++) dp[i][j] = 0;
  dp[0][0] = 1;
  for (int i = 0; i < (n); i++) {
    for (int j = 0; j < (n + 1); j++) {
      dp[i][j] = min(dp[i][j], MAX);
      if (result[i]) {
        if (j + result[i] >= 0) {
          dp[i + 1][j + result[i]] += dp[i][j];
        }
      } else {
        if (j) dp[i + 1][j - 1] += dp[i][j];
        dp[i + 1][j + 1] += dp[i][j];
      }
    }
  }
  return dp[n][0];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m;
  long long k;
  scanf("%d%d%lld", &n, &m, &k);
  vector<pair<int, pair<int, int>>> priors;
  for (int i = 0; i < (n); i++)
    for (int j = 0; j < (m); j++) {
      int x;
      scanf("%d", &x);
      priors.push_back({x, {i, j}});
    }
  sort((priors).begin(), (priors).end());
  for (auto z : priors) {
    int pos = z.second.first + z.second.second;
    if (result[pos]) continue;
    result[pos] = 1;
    long long cnt = f(n + m - 1);
    if (cnt >= k) continue;
    result[pos] = -1;
    k -= cnt;
  }
  for (int i = 0; i < (n); i++) {
    for (int j = 0; j < (m); j++) {
      int pos = i + j;
      printf("%c", result[pos] == 1 ? '(' : ')');
    }
    puts("");
  }
}
