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 ll = long long;
using ld = long double;
using ull = unsigned long long;
using namespace std;
const int N = 102;
int n, m, c[N][N], a[2 * N], ans[2 * N];
ll dp[2 * N][N], K;
ll calWays(int p, int bal) {
  if (p == 0) return (bal == 0);
  ll& res = dp[p][bal];
  if (res != -1) return res;
  res = 0;
  if (bal > 0 && (ans[p] == -1 || ans[p] == 0)) res += calWays(p - 1, bal - 1);
  if (bal < (n + m - 1) / 2 && (ans[p] == -1 || ans[p] == 1))
    res += calWays(p - 1, bal + 1);
  return min(K + 1, res);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m >> K;
  for (int i = (1); i <= (n); ++i)
    for (int j = (1); j <= (m); ++j) cin >> c[i][j];
  for (int i = (1); i <= (n + m - 1); ++i) a[i] = 1e9, ans[i] = -1;
  for (int i = (1); i <= (n); ++i)
    for (int j = (1); j <= (m); ++j) a[i + j - 1] = min(a[i + j - 1], c[i][j]);
  for (int t = (1); t <= (n + m - 1); ++t) {
    int mn = 1e9, mni = 0;
    for (int i = (1); i <= (n + m - 1); ++i)
      if (ans[i] == -1 && mn > a[i]) mn = a[i], mni = i;
    ans[mni] = 0;
    for (int i = (0); i <= (n + m - 1); ++i)
      for (int bal = (0); bal <= ((n + m) / 2); ++bal) dp[i][bal] = -1;
    ll ways = calWays(n + m - 1, 0);
    if (ways < K) {
      K -= ways;
      ans[mni] = 1;
    }
  }
  for (int i = (1); i <= (n); ++i) {
    for (int j = (1); j <= (m); ++j) cout << (ans[i + j - 1] ? ')' : '(');
    if (i < n) cout << '\n';
  }
  return 0;
}
