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;
static const int INF = 500000000;
template <class T>
void debug(T a, T b) {
  for (; a != b; ++a) cerr << *a << ' ';
  cerr << endl;
}
static const long long int BIG = 2.5e18;
int n, m;
long long int k;
int buf[105][105];
int pri[205];
int len;
int seq[205], tmp[205], sum[205];
long long int dp[205][205];
void add(long long int &a, long long int b) {
  a = a + b;
  if (a >= BIG) a = BIG;
}
long long int check() {
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int i = 0; i < len; ++i)
    for (int j = 0; j < i + 1; ++j)
      if (dp[i][j] > 0) {
        if (j > 0 && (seq[i] == 0 || seq[i] == -1))
          add(dp[i + 1][j - 1], dp[i][j]);
        if (seq[i] == 1 || seq[i] == -1) add(dp[i + 1][j + 1], dp[i][j]);
      }
  return dp[len][0];
}
int main() {
  for (int i = 0; i < 205; ++i) pri[i] = INF;
  cin >> n >> m >> k;
  --k;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < m; ++j) {
      int a;
      cin >> a;
      pri[i + j] = min(pri[i + j], a);
    }
  memset(seq, -1, sizeof(seq));
  len = n + m - 1;
  for (int hoge = 0; hoge < len; ++hoge) {
    int mini = INF, who;
    for (int i = 0; i < len; ++i)
      if (seq[i] == -1 && pri[i] < mini) {
        mini = pri[i];
        who = i;
      }
    seq[who] = 1;
    long long int val = check();
    if (val <= k) {
      seq[who] = 0;
      k -= val;
    }
  }
  char conv[5];
  conv[0] = ')';
  conv[1] = '(';
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < m; ++j) putchar(conv[seq[i + j]]);
    putchar('\n');
  }
  return 0;
}
