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 int max_n = 205;
const int inf = 1e9;
const long long mx = LLONG_MAX;
int n, m;
long long k;
int a[max_n][max_n];
int md[max_n];
long long dp[max_n][max_n][2], mdp[max_n][max_n], rdp[max_n][max_n][2],
    mrdp[max_n][max_n];
pair<int, int> P[max_n];
bool b[max_n], s[max_n];
int dx[2] = {-1, 1};
char res[max_n][max_n];
int main() {
  scanf("%d%d", &n, &m);
  cin >> k;
  int N = n + m - 1;
  for (int i = 0; i < N; i++) md[i] = inf;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      scanf("%d", &a[i][j]);
      md[i + j] = min(md[i + j], a[i][j]);
    }
  for (int i = 0; i < N; i++) P[i] = make_pair(md[i], i);
  sort(P, P + N);
  for (int z = 0; z < N; z++) {
    int ind = P[z].second + 1;
    for (int i = 0; i <= N; i++)
      for (int j = 0; j <= N; j++) {
        mdp[i][j] = 0;
        mrdp[i][j] = 0;
        dp[i][j][0] = 0;
        dp[i][j][1] = 0;
        rdp[i][j][0] = 0;
        rdp[i][j][1] = 0;
      }
    mdp[0][0] = 1;
    mrdp[N + 1][0] = 1;
    for (int i = 1; i <= N; i++)
      for (int j = 0; j <= i; j++) {
        if (b[i] and j + dx[s[i]] >= 0 and j + dx[s[i]] < i)
          dp[i][j][s[i]] = mdp[i - 1][j + dx[s[i]]];
        else if (!b[i]) {
          dp[i][j][0] = ((j > 0) ? mdp[i - 1][j - 1] : 0);
          dp[i][j][1] = ((j < i - 1) ? mdp[i - 1][j + 1] : 0);
        }
        long long t1 = dp[i][j][0], t2 = dp[i][j][1];
        mdp[i][j] = (mx - t1 < t2) ? mx : dp[i][j][0] + dp[i][j][1];
      }
    for (int i = N; i >= 1; i--)
      for (int j = 0; j <= N - i + 1; j++) {
        if (b[i] and j - dx[s[i]] >= 0 and j - dx[s[i]] < N - i + 1)
          rdp[i][j][s[i]] = mrdp[i + 1][j - dx[s[i]]];
        else if (!b[i]) {
          rdp[i][j][1] = ((j > 0) ? mrdp[i + 1][j - 1] : 0);
          rdp[i][j][0] = ((j < N - i) ? mrdp[i + 1][j + 1] : 0);
        }
        long long t1 = rdp[i][j][0], t2 = rdp[i][j][1];
        mrdp[i][j] = (mx - t1 < t2) ? mx : rdp[i][j][0] + rdp[i][j][1];
      }
    long long nways = 0ll;
    bool overflow = 0;
    for (int j = 1; j <= ind; j++) {
      long long t1 = dp[ind][j][0], t2 = rdp[ind][j - 1][0];
      if (t1 > 0 and (mx / t1 < t2 or mx - t1 * t2 < nways)) {
        overflow = 1;
        break;
      }
      nways += dp[ind][j][0] * rdp[ind][j - 1][0];
    }
    if (overflow or nways >= k)
      s[ind] = 0;
    else {
      s[ind] = 1;
      k -= nways;
    }
    b[ind] = 1;
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) res[i][j] = (s[i + j + 1] == 0) ? '(' : ')';
  for (int i = 0; i < n; i++) printf("%s\n", res[i]);
  return 0;
}
