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;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 102;
int n, m;
long long u;
int a[N][N];
char ans[N + N];
int minu[N + N];
long long dp[N + N][N + N];
void solv() {
  scanf("%d%d%lld", &n, &m, &u);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      scanf("%d", &a[i][j]);
    }
  }
  for (int i = 0; i < n + m - 1; ++i) {
    minu[i] = N * N * N;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      minu[i + j] = min(minu[i + j], a[i][j]);
    }
  }
  vector<pair<int, int> > v;
  for (int i = 0; i < n + m - 1; ++i) {
    v.push_back(make_pair(minu[i], i));
  }
  sort(v.begin(), v.end());
  for (int ii = 0; ii < v.size(); ++ii) {
    int i = v[ii].second;
    ans[i] = '(';
    memset(dp, 0, sizeof dp);
    dp[v.size()][0] = 1;
    for (int j = v.size() - 1; j >= 0; --j) {
      for (int k = 0; k < v.size(); ++k) {
        if (ans[j] == '(') {
          if (k - 1 >= 0) {
            dp[j][k - 1] += dp[j + 1][k];
            dp[j][k - 1] = min(dp[j][k - 1], u + 1);
          }
        } else if (ans[j] == ')') {
          dp[j][k + 1] += dp[j + 1][k];
          dp[j][k + 1] = min(dp[j][k + 1], u + 1);
        } else {
          if (k - 1 >= 0) {
            dp[j][k - 1] += dp[j + 1][k];
            dp[j][k - 1] = min(dp[j][k - 1], u + 1);
          }
          dp[j][k + 1] += dp[j + 1][k];
          dp[j][k + 1] = min(dp[j][k + 1], u + 1);
        }
      }
    }
    if (dp[0][0] >= u) continue;
    ans[i] = ')';
    u -= dp[0][0];
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      printf("%c", ans[i + j]);
    }
    printf("\n");
  }
}
int main() {
  solv();
  return 0;
}
