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 double EPS = 1e-9;
int cmp(double x, double y = 0, double tol = EPS) {
  return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1;
}
const int MAXN = 205;
int priority[MAXN];
char str[MAXN];
int permutation[MAXN];
long long ways[MAXN][MAXN];
const long long INF = 1000000000000000001LL;
bool prioritary(int i, int j) { return priority[i] < priority[j]; }
void add(long long &where, const long long what) {
  where += what;
  if (where > INF) where = INF;
}
long long count(int len) {
  memset(ways, 0, sizeof ways);
  ways[0][0] = 1;
  for (int i = 0; i < len; ++i) {
    const char next = str[i];
    for (int open = 0; open <= len; ++open) {
      if (ways[i][open] == 0) continue;
      if (next != ')') add(ways[i + 1][open + 1], ways[i][open]);
      if (next != '(' and open > 0) add(ways[i + 1][open - 1], ways[i][open]);
    }
  }
  return ways[len][0];
}
int main() {
  int n, m;
  long long k;
  cin >> n >> m >> k;
  assert(k < INF);
  assert((n + m) % 2 == 1);
  for (int i = 0; i < n + m - 1; ++i) {
    priority[i] = n * m + 1;
    permutation[i] = i;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      int x;
      cin >> x;
      priority[i + j] = min(priority[i + j], x);
    }
  }
  sort(permutation, permutation + n + m - 1, prioritary);
  for (int i = 0; i < n + m - 1; ++i) str[i] = '*';
  str[n + m - 1] = '\0';
  for (int i = 0; i < n + m - 1; ++i) {
    int pos = permutation[i];
    str[pos] = '(';
    long long add = count(n + m - 1);
    if (k > add) {
      str[pos] = ')';
      k -= add;
    }
  }
  assert(k == 1);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) {
      printf("%c", str[i + j]);
    }
    printf("\n");
  }
  return 0;
}
