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;
static const double EPS = 1e-8;
long long memo[210][210];
long long calc(int d, int open, string &s) {
  int n = s.size();
  if (d == n) {
    if (open == 0)
      return 1;
    else
      return 0;
  }
  if (memo[d][open] >= 0) return memo[d][open];
  long long res = 0;
  if (s[d] != ')') res += calc(d + 1, open + 1, s);
  if (s[d] != '(' && open > 0) res += calc(d + 1, open - 1, s);
  if (s[d] == ')' && open == 0) res = 0;
  if (res > 1000000000000000001LL) res = 1000000000000000001LL;
  memo[d][open] = res;
  return res;
}
int main() {
  istream &fin = cin;
  ostream &fout = cout;
  FILE *fpin = stdin;
  FILE *fpout = stdout;
  int n, m;
  long long k;
  fin >> n >> m >> k;
  vector<pair<int, int> > p(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    p[i].first = 1000000000;
    p[i].second = i;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int pv;
      fin >> pv;
      p[i + j].first = min(p[i + j].first, pv);
    }
  }
  sort(p.begin(), p.end());
  string s(n + m - 1, ' ');
  for (int i = 0; i < n + m - 1; i++) {
    s[p[i].second] = '(';
    memset(memo, -1, sizeof(memo));
    long long cnt = calc(0, 0, s);
    if (cnt < k) {
      s[p[i].second] = ')';
      k -= cnt;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      fout << s[i + j];
    }
    fout << endl;
  }
}
