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:50000000")
using namespace std;
long long n, m;
long long k;
long long A[402][402];
long long B[402];
long long numbers[402];
long long f[402][402];
const long long INF = 2147483647;
vector<pair<long long, long long> > R;
string s;
long long rec(long long i, long long j) {
  long long res = 0;
  if (j < 0 || j > i || i > R.size() || i < 0 || j > R.size() - i) return 0;
  if (f[i][j] != -1) return f[i][j];
  if (i - 1 >= 0 && s[i - 1] != ')') res += rec(i - 1, j - 1);
  if (i - 1 >= 0 && s[i - 1] != '(') res += rec(i - 1, j + 1);
  if (res > k) res = k;
  return f[i][j] = res;
}
int main() {
  cin >> n >> m;
  cin >> k;
  long long sz = n + m - 1;
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) cin >> A[i][j];
  for (long long i = 0; i < n; i++) {
    B[i] = 2147483647;
    for (long long j = 0; j < m; j++)
      if (i - j >= 0) B[i] = min(B[i], A[i - j][j]);
  }
  for (long long j = 1; j < m; j++) {
    B[n + j - 1] = 2147483647;
    for (long long i = n - 1; i >= 0; i--) {
      if (j + (n - 1) - i < m)
        B[n + j - 1] = min(B[n + j - 1], A[i][j + (n - 1) - i]);
    }
  }
  R.resize(sz);
  s.resize(R.size() + 2);
  for (long long i = 0; i < R.size(); i++) R[i].first = B[i], R[i].second = i;
  sort(R.begin(), R.end());
  for (long long I = 0; I < R.size(); I++) {
    s[R[I].second] = '(';
    memset(f, -1, sizeof f);
    f[0][0] = 1;
    long long em = rec(R.size(), 0);
    if (em < k) {
      k -= em;
      s[R[I].second] = ')';
    }
  }
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) cout << s[i + j];
    cout << endl;
  }
  return 0;
}
