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 int P = 1e9 + 7;
int add(int a, int b) {
  if ((a += b) >= P) a -= P;
  return a;
}
int sub(int a, int b) {
  if ((a -= b) < 0) a += P;
  return a;
}
int mul(int a, int b) { return 1ll * a * b % P; }
int kpow(int a, int b) {
  int r = 1;
  for (; b; b >>= 1, a = mul(a, a)) {
    if (b & 1) r = mul(r, a);
  }
  return r;
}
const int N = 111;
int n, m;
int p[N][N], a[N << 1], vis[N << 1], id[N << 1];
long long k, inf;
long long f[N << 1][N << 1];
vector<int> V;
long long calc() {
  memset(f, 0, sizeof(f));
  f[0][0] = 1;
  for (int i = (1); i < (n + m); i++)
    for (int j = (0); j < (n + m); j++) {
      if (vis[i] == 0 || vis[i] == -1)
        if (j - 1 >= 0) f[i][j] = min(f[i][j] + f[i - 1][j - 1], inf);
      if (vis[i] == 1 || vis[i] == -1)
        if (j + 1 < n + m) f[i][j] = min(f[i][j] + f[i - 1][j + 1], inf);
    }
  return f[n + m - 1][0];
}
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  cin >> n >> m >> k;
  inf = k + 1;
  memset(a, 0x3f, sizeof(a));
  memset(vis, -1, sizeof(vis));
  for (int i = (0); i < (n); i++)
    for (int j = (0); j < (m); j++) {
      cin >> p[i][j];
      a[i + j] = min(a[i + j], p[i][j]);
    }
  for (int i = (0); i < (n + m - 1); i++) V.push_back(a[i]);
  sort(V.begin(), V.end());
  for (int i = (0); i < (n + m - 1); i++)
    a[i] = lower_bound(V.begin(), V.end(), a[i]) - V.begin() + 1,
    id[a[i]] = i + 1;
  for (int i = (1); i < (n + m); i++) {
    vis[id[i]] = 0;
    long long t = calc();
    if (t >= k) continue;
    k -= t;
    vis[id[i]] = 1;
  }
  for (int i = (0); i < (n); i++) {
    for (int j = (0); j < (m); j++) cout << (vis[i + j + 1] ? ")" : "(");
    cout << "\n";
  }
  return 0;
}
