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;
int p[105][105];
char s[105][105];
int n, m;
long long k;
void color(int x, int y, char c) {
  while (x < n && y >= 0) {
    s[x][y] = c;
    x++;
    y--;
  }
}
vector<pair<pair<int, int>, pair<int, int> > > v;
vector<int> vals;
long long mem[305][305];
int vis[305][305];
int id;
long long add(long long x, long long y) {
  if (x < 0 || y < 0) return -1;
  long long z = x + y;
  if (z >= k) return -1;
  return z;
}
long long solve(int ind, int r) {
  if (r < 0) return 0;
  if (ind >= int(vals.size())) return r == 0;
  if (vis[ind][r] == id) return mem[ind][r];
  vis[ind][r] = id;
  long long ans = 0;
  if (vals[ind] != 1) ans = add(ans, solve(ind + 1, r + 1));
  if (vals[ind] != 0) ans = add(ans, solve(ind + 1, r - 1));
  return mem[ind][r] = ans;
}
void gen(int ind) {
  if (ind >= int(vals.size())) return;
  vals[v[ind].first.second] = 0;
  id++;
  long long tmp = solve(0, 0);
  if (tmp == -1) {
    color(v[ind].second.first, v[ind].second.second, '(');
    gen(ind + 1);
  } else {
    vals[v[ind].first.second] = 1;
    k -= tmp;
    color(v[ind].second.first, v[ind].second.second, ')');
    gen(ind + 1);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> m;
  cin >> k;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> p[i][j];
  for (int j = 0; j < m; j++) {
    int x = 0, y = j, pr = n * m + 1;
    while (x < n && y >= 0) {
      pr = min(pr, p[x][y]);
      x++;
      y--;
    }
    v.push_back(make_pair(make_pair(pr, v.size()), make_pair(0, j)));
    vals.push_back(-1);
  }
  for (int i = 1; i < n; i++) {
    int x = i, y = m - 1, pr = n * m + 1;
    while (x < n && y >= 0) {
      pr = min(pr, p[x][y]);
      x++;
      y--;
    }
    v.push_back(make_pair(make_pair(pr, v.size()), make_pair(i, m - 1)));
    vals.push_back(-1);
  }
  sort(v.begin(), v.end());
  gen(0);
  for (int i = 0; i < n; i++) cout << s[i] << endl;
  return 0;
}
