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;
inline long long in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline long long lin() {
  long long x;
  scanf("%lld", &x);
  return x;
}
const long long maxn = 200 + 10;
const long long inf = 1e18 + 1;
long long a[maxn][maxn], mini[maxn], res[maxn], dp[maxn][maxn], id[maxn],
    what[maxn];
long long N;
inline void calcDp() {
  memset(dp, 0, sizeof dp);
  dp[N][0] = 1;
  for (long long i = N - 1; i >= 0; i--) {
    for (long long j = 0; j <= i; j++) {
      dp[i][j] = min(dp[i + 1][j + 1] * bool(what[i] != 1) +
                         (j && what[i] != 0 ? dp[i + 1][j - 1] : 0),
                     inf);
    }
  }
}
int32_t main() {
  long long n = in(), m = in(), k = lin();
  N = n + m - 1;
  memset(mini, 63, sizeof mini);
  memset(res, -1, sizeof res);
  memset(what, -1, sizeof what);
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < m; j++) a[i][j] = in();
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < m; j++) mini[i + j] = min(mini[i + j], a[i][j]);
  }
  iota(id, id + n + m - 1, 0);
  sort(id, id + n + m - 1, [](const long long &a, const long long &b) {
    return mini[a] < mini[b];
  });
  for (long long _ = 0; _ < n + m - 1; _++) {
    long long i = id[_];
    what[i] = 0;
    calcDp();
    if (dp[0][0] >= k) continue;
    k -= dp[0][0];
    what[i] = 1;
  }
  for (long long i = 0; i < n; i++, cout << "\n") {
    for (long long j = 0; j < m; j++) {
      cout << (what[i + j] == 0 ? '(' : ')');
    }
  }
}
