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>
const long long INF = 1e18;
std::pair<int, int> p[205];
char ans[205];
void add(long long &x, long long val) {
  if (x + val > INF) {
    x = INF;
  } else
    x += val;
}
long long calc(int n) {
  static long long dp[205][205];
  std::fill(dp[0], dp[n + 1], 0);
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j <= i; j++) {
      long long now = dp[i][j];
      if (!now) continue;
      if (ans[i] == '(') {
        add(dp[i + 1][j + 1], now);
      }
      if (ans[i] == '?') {
        add(dp[i + 1][j + 1], now);
        if (j > 0) add(dp[i + 1][j - 1], now);
      }
      if (ans[i] == ')' && j > 0) {
        add(dp[i + 1][j - 1], now);
      }
    }
  }
  return dp[n][0];
}
int main() {
  int N, M;
  long long K;
  std::cin >> N >> M >> K;
  for (int i = 0; i < N + M; i++) p[i].first = 1e9;
  for (int i = 0; i < N; i++) {
    for (int j = 0, x; j < M; j++) {
      std::cin >> x;
      p[i + j].first = std::min(p[i + j].first, x);
      p[i + j].second = i + j;
    }
  }
  int n = N + M - 1;
  std::sort(p, p + n);
  std::fill(ans, ans + n, '?');
  for (int i = 0; i < n; i++) {
    ans[p[i].second] = '(';
    long long k = calc(n);
    if (k < K) {
      K -= k;
      ans[p[i].second] = ')';
    }
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < M; j++) {
      putchar(ans[i + j]);
    }
    puts("");
  }
  return 0;
}
