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 l;
vector<int> an;
long long res[200][200];
void sr(long long& a, long long b) {
  a += b;
  if (a > 1000000000000000001LL) a = 1000000000000000001LL;
}
long long check() {
  for (int i = 0; i < l + 1; ++i)
    for (int j = 0; j < l + 1; ++j) res[i][j] = 0;
  res[0][0] = 1;
  for (int i = 0; i < l; ++i)
    for (int j = 0; j <= i; j++)
      if (res[i][j]) {
        if (an[i] == -1 || an[i] == 0) sr(res[i + 1][j + 1], res[i][j]);
        if (j && (an[i] == -1 || an[i] == 1)) sr(res[i + 1][j - 1], res[i][j]);
      }
  return res[l][0];
}
int main(int argc, char** argv) {
  int n, m, x;
  long long k;
  cin >> n >> m >> k;
  l = m + n - 1;
  an = vector<int>(l, -1);
  vector<int> pr(l, n * m + 1);
  vector<long long> cat(l / 2 + 1, 0);
  cat[0] = 1;
  cat[1] = 1;
  for (int i = 2; 2 * i <= l; i++) {
    long long sum = 0;
    for (int j = 0; j < i; j++) sum += cat[j] * cat[i - j - 1];
    cat[i] = sum;
  }
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      cin >> x;
      int num = (i + j) % l;
      pr[num] = min(pr[num], x);
    }
  int ctm = 0;
  for (int it = 0; it < l; ++it) {
    int cm = -1;
    for (int i = 0; i < l; ++i)
      if (pr[i] > ctm) {
        if (cm == -1 || pr[i] < pr[cm]) cm = i;
      }
    int nextp = cm + 1;
    an[cm] = 0;
    long long sr = check();
    if (sr < k) {
      an[cm] = 1;
      k -= sr;
    }
    ctm = pr[cm];
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) printf("%c", '(' + an[(i + j) % l]);
    printf("\n");
  }
  return 0;
}
