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>
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
using namespace std;
const long long int N = 1e2 + 30, mod = 1e9 + 7, inf = 1e9;
unsigned long long int C = 2e18;
int p[N][N], d[210];
unsigned long long int dp[2 * N][2 * N];
char ans[2 * N], table[N][N];
void ovf(unsigned long long int& a) { a = min(a, C); }
int main() {
  int n, m;
  unsigned long long int T;
  cin >> n >> m >> T;
  ovf(T);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> p[i][j];
    }
  }
  for (int i = 0; i < n; i++) {
    d[i] = p[i][0];
    int x = 0, y = i;
    while (y >= 0 && x < m) {
      d[i] = min(d[i], p[y][x]);
      y--;
      x++;
    }
  }
  for (int i = 1; i < m; i++) {
    d[n + i - 1] = p[n - 1][i];
    int x = i, y = n - 1;
    while (y >= 0 && x < m) {
      d[n + i - 1] = min(d[n + i - 1], p[y][x]);
      y--;
      x++;
    }
  }
  ans[0] = '(';
  ans[n + m - 2] = ')';
  int to = 0;
  for (int i = 1; i < m + n - 2; i++) {
    memset(dp, 0, sizeof dp);
    dp[0][1] = 1;
    int mi = inf, ind = -1;
    int t = 0;
    for (int j = 1; j < n + m - 1; j++)
      if (ans[j] != ')' && ans[j] != '(') {
        if (mi > d[j]) {
          mi = d[j];
          ind = j;
        }
      }
    ans[ind] = '(';
    for (int j = 1; j < n + m - 1; j++) {
      for (int k = (j + 1) / 2 + (j + 1) % 2; k < j + 2; k++) {
        if (ans[j] == '(') {
          dp[j][k] = dp[j - 1][k - 1];
        } else if (ans[j] == ')') {
          if (k >= j - k)
            dp[j][k] = dp[j - 1][k];
          else
            dp[j][k] = 0;
        } else {
          dp[j][k] = dp[j - 1][k - 1];
          if (k >= j - k) dp[j][k] += dp[j - 1][k];
          ovf(dp[j][k]);
        }
      }
    }
    unsigned long long int cnt = dp[n + m - 2][(n + m - 1) / 2];
    if (cnt < T && i - to < (n + m - 1) / 2) {
      T -= cnt;
      ans[ind] = ')';
    } else {
      ans[ind] = '(';
      to++;
    }
    if (to == (m + n - 1) / 2 - 1) break;
  }
  for (int i = 0; i < n + m; i++) {
    if (ans[i] != '(') ans[i] = ')';
  }
  for (int i = 0; i < n; i++) {
    int x = 0, y = i;
    while (x < m && y >= 0) {
      table[y][x] = ans[i];
      y--;
      x++;
    }
  }
  for (int i = 1; i < m; i++) {
    int x = i, y = n - 1;
    while (x < m && y >= 0) {
      table[y][x] = ans[n + i - 1];
      x++;
      y--;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) cout << table[i][j];
    cout << '\n';
  }
}
