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 long long inf = 2e18;
const int N = 2e2 + 22;
long long mem[N][N];
int p[N], len, pos[N];
char s[N];
long long dp(int i, int cur) {
  if (mem[i][cur] != -1) return mem[i][cur];
  long long &ret = mem[i][cur];
  if (i == len) {
    if (s[i] == '(') return ret = 0;
    if (s[i] == ')' || s[i] == '?') return ret = (cur == 1);
    return ret = 0;
  }
  ret = 0;
  if (s[i] == '(' || s[i] == '?') {
    ret += dp(i + 1, cur + 1);
  }
  if (s[i] == ')' || s[i] == '?') {
    if (cur > 0) ret += dp(i + 1, cur - 1);
  }
  if (ret > inf) ret = inf;
  return ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout << setprecision(32);
  int n, m;
  long long k;
  cin >> n >> m >> k;
  memset(p, 0x3f, sizeof(p));
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      int x;
      cin >> x;
      p[i + j - 1] = min(p[i + j - 1], x);
    }
  }
  len = n + m - 1;
  vector<pair<int, int> > vec;
  for (int i = 1; i <= len; i++) {
    s[i] = '(';
    vec.push_back({p[i], i});
  }
  sort(vec.rbegin(), vec.rend());
  long long tot = 0;
  for (int i = 1; i <= len; i++) {
    s[vec[i - 1].second] = ')';
    memset(mem, -1, sizeof(mem));
    long long val = dp(1, 0);
    if (tot + val >= k) {
      for (int j = i; j >= 1; j--) {
        memset(mem, -1, sizeof(mem));
        s[vec[j - 1].second] = '(';
        long long val = dp(1, 0);
        if (val < k) {
          k -= val;
          s[vec[j - 1].second] = ')';
        }
      }
      break;
    } else {
      tot += val;
    }
    s[vec[i - 1].second] = '?';
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      cout << s[i + j - 1];
    }
    cout << '\n';
  }
  return 0;
}
