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;
const long long N = 222, inf = 1e18 + 7;
long long a[N][N], trn[N], n;
char c[N], ans[N][N];
long long _dp[N][2 * N];
long long fi, se, k;
long long dp(long long x, long long y) {
  if (x == -1 && y == 0) return 1;
  if (min(x, y) < 0) return 0;
  if (_dp[x][y] != -1) return _dp[x][y];
  if (c[x] == ')')
    _dp[x][y] = dp(x - 1, y + 1);
  else if (c[x] == '(')
    _dp[x][y] = dp(x - 1, y - 1);
  else
    _dp[x][y] = dp(x - 1, y + 1) + dp(x - 1, y - 1);
  if (_dp[x][y] > inf) _dp[x][y] = inf;
  return _dp[x][y];
}
long long calc() {
  memset(_dp, -1, sizeof _dp);
  return dp(n - 1, 0);
}
bool check(long long x, long long y) {
  return (x < fi && y < se && min(x, y) > -1);
}
int32_t main() {
  cin >> fi >> se >> k;
  n = fi + se - 1;
  memset(trn, 63, sizeof trn);
  for (long long i = 0; i < fi; i++)
    for (long long j = 0; j < se; j++) cin >> a[i][j];
  for (long long i = 0; i < se; i++)
    for (long long j = 0; check(j, i - j); j++)
      trn[i] = min(trn[i], a[j][i - j]);
  for (long long i = 1; i < fi; i++)
    for (long long j = se - 1; check(i + se - 1 - j, j); j--)
      trn[se + i - 1] = min(trn[se + i - 1], a[i + se - 1 - j][j]);
  vector<pair<long long, long long> > vec;
  for (long long i = 0; i < n; i++) vec.push_back({trn[i], i}), c[i] = '?';
  sort(vec.begin(), vec.end());
  for (auto i : vec) {
    c[i.second] = '(';
    long long x = calc();
    if (x < k) k -= x, c[i.second] = ')';
  }
  for (long long i = 0; i < se; i++)
    for (long long j = 0; check(j, i - j); j++) ans[j][i - j] = c[i];
  for (long long i = 1; i < fi; i++)
    for (long long j = se - 1; check(i + se - 1 - j, j); j--)
      ans[i + se - 1 - j][j] = c[se + i - 1];
  for (long long i = 0; i < fi; i++, cout << '\n')
    for (long long j = 0; j < se; j++) cout << ans[i][j];
}
