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>
#pragma comment(linker, "/stack:64000000")
using namespace std;
const unsigned long long INF = 1001001001001001001LL;
struct st {
  int i, j, p;
  st() {}
  st(int i, int j, int p) : i(i), j(j), p(p) {}
};
bool operator<(const st& a, const st& b) { return a.p < b.p; }
vector<st> a;
int used[300], n, m;
unsigned long long d[300][300], k;
unsigned long long calc() {
  memset(d, 0, sizeof d);
  d[0][0] = 1;
  for (int i = 0; i < (int)n + m - 1; i++)
    for (int j = 0; j < (int)i + 1; j++) {
      if (d[i][j] == 0) continue;
      if (used[i] != -1) {
        d[i + 1][j + 1] += d[i][j];
        if (d[i + 1][j + 1] > INF) d[i + 1][j + 1] = INF;
      }
      if (j > 0 && used[i] != 1) {
        d[i + 1][j - 1] += d[i][j];
        if (d[i + 1][j + 1] > INF) d[i + 1][j + 1] = INF;
      }
    }
  return d[n + m - 1][0];
}
int main() {
  cin >> n >> m >> k;
  k--;
  for (int i = 0; i < (int)n; i++)
    for (int j = 0; j < (int)m; j++) {
      int v;
      cin >> v;
      a.push_back(st(i, j, v));
    }
  sort((a).begin(), (a).end());
  for (int i = 0; i < (int)(int)(a).size(); i++) {
    while (i < (int)(a).size() && used[a[i].i + a[i].j]) i++;
    if (i == (int)(a).size()) break;
    int pos = a[i].i + a[i].j;
    used[pos] = 1;
    unsigned long long cur = calc();
    if (k >= cur) {
      used[pos] = -1;
      k -= cur;
    }
  }
  for (int i = 0; i < (int)n; i++) {
    for (int j = 0; j < (int)m; j++)
      if (used[i + j] == 1)
        cout << "(";
      else
        cout << ")";
    cout << endl;
  }
}
