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;
template <class T>
inline void checkmin(T &a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T &a, T b) {
  if (b > a) a = b;
}
int a[111 * 2];
char c[111 * 2];
long long pre[111 * 2], dp[111 * 2];
int N, M;
long long K;
long long inf64 = 1ll * 1000000001 * 1000000001;
long long doit() {
  memset((dp), 0, sizeof(dp));
  dp[0] = 1;
  for (int i = (0); i < (int)(N + M - 1); i++) {
    for (int j = (0); j < (int)(N + M); j++) pre[j] = dp[j], dp[j] = 0;
    bool f1 = false, f2 = false;
    f1 = (c[i] == '(' || c[i] == 0);
    f2 = (c[i] == ')' || c[i] == 0);
    if (f1)
      for (int j = (0); j < (int)(N + M); j++)
        dp[j + 1] = min(dp[j + 1] + pre[j], inf64);
    if (f2)
      for (int j = (1); j < (int)(N + M); j++)
        dp[j - 1] = min(dp[j - 1] + pre[j], inf64);
  }
  return dp[0];
}
int main() {
  cin >> N >> M >> K;
  K--;
  for (int i = (0); i < (int)(111 * 2); i++) a[i] = 1000000001;
  memset((c), 0, sizeof(c));
  int v;
  for (int i = (0); i < (int)(N); i++)
    for (int j = (0); j < (int)(M); j++) scanf("%d", &v), checkmin(a[i + j], v);
  vector<pair<int, int> > vp;
  for (int i = (0); i < (int)(N + M - 1); i++) vp.push_back(make_pair(a[i], i));
  sort((vp).begin(), (vp).end());
  for (int i = (0); i < (int)(N + M - 1); i++) {
    int idx = vp[i].second;
    c[idx] = '(';
    long long shu = doit();
    if (K >= shu) K -= shu, c[idx] = ')';
  }
  for (int i = (0); i < (int)(N); i++) {
    for (int j = (0); j < (int)(M); j++) printf("%c", c[i + j]);
    printf("\n");
  }
  return 0;
}
