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 maxN = 2e2 + 5;
const long long INF = 1e18;
const long long MOD = 1e9 + 7;
long long gcd(long long a, long long b) { return !b ? a : gcd(b, a % b); }
long long sq(long long x) { return (x * x) % MOD; }
long long modP(long long a, long long b) {
  return (!b ? 1 : (sq(modP(a, b / 2)) * (b % 2 ? a : 1)) % MOD);
}
long long pr[maxN], c[maxN], dp[maxN][maxN];
bool cmp(long long a, long long b) { return (pr[a] < pr[b]); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m, inp;
  cin >> n >> m;
  long long k;
  cin >> k;
  memset(pr, 63, sizeof pr);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> inp;
      pr[i + j] = min(pr[i + j], inp);
    }
  }
  for (int i = 0; i < maxN; i++) {
    c[i] = i;
  }
  sort(c, c + n + m - 1, cmp);
  string s;
  for (int i = 0; i < n + m - 1; i++) {
    s += '?';
  }
  for (int x = 0; x < n + m - 1; x++) {
    s[c[x]] = '(';
    memset(dp, 0, sizeof dp);
    dp[1][0] = 1;
    for (int i = 2; i <= n + m; i++) {
      for (int j = 0; j <= i; j++) {
        if (s[i - 2] != '?') {
          dp[i][j] = (s[i - 2] == '(' ? (j == 0 ? 0 : dp[i - 1][j - 1])
                                      : dp[i - 1][j + 1]);
          dp[i][j] = min(INF, dp[i][j]);
          continue;
        }
        if (j == 0) {
          dp[i][j] = dp[i - 1][j + 1];
        } else
          dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j + 1];
        dp[i][j] = min(INF, dp[i][j]);
      }
    }
    if (dp[n + m][0] < k) {
      s[c[x]] = ')';
      k -= dp[n + m][0];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << s[i + j];
    }
    cout << endl;
  }
  return 0;
}
