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>
const long long MaxN = 205;
const long long lim = 1e18 + 5;
template <class t>
inline void read(t &s) {
  s = 0;
  register long long f = 1;
  register char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  s *= f;
  return;
}
template <class t, class... A>
inline void read(t &x, A &...a) {
  read(x);
  read(a...);
}
template <class t>
inline void write(t x) {
  if (x < 0) putchar('-'), x = -x;
  long long buf[21], top = 0;
  while (x) buf[++top] = x % 10, x /= 10;
  if (!top) buf[++top] = 0;
  while (top) putchar(buf[top--] ^ '0');
  return;
}
inline void setIn(std::string s) {
  freopen(s.c_str(), "r", stdin);
  return;
}
inline void setOut(std::string s) {
  freopen(s.c_str(), "w", stdout);
  return;
}
inline void setIO(std::string s = "") {
  setIn(s + ".in");
  setOut(s + ".out");
  return;
}
template <class t>
inline bool checkmin(t &x, t y) {
  if (x > y) {
    x = y;
    return 1;
  }
  return 0;
}
template <class t>
inline bool checkmax(t &x, t y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
inline long long lowbit(long long x) { return x & (-x); }
long long a[MaxN][MaxN], p[MaxN], t[MaxN], n, m, K, q;
long long b[MaxN], f[MaxN][MaxN];
inline void add(long long &x, long long y) { (x += y) >= lim && (x = lim); }
inline long long calc() {
  std::memset(f, 0, sizeof f);
  f[0][0] = 1;
  for (long long i = 1; i <= q; ++i) {
    if (b[i] >= 0)
      for (long long j = 1; j <= q; ++j) add(f[i][j], f[i - 1][j - 1]);
    if (b[i] <= 0)
      for (long long j = 0; j < q; ++j) add(f[i][j], f[i - 1][j + 1]);
  }
  return f[q][0];
}
signed main(void) {
  read(n, m, K);
  for (long long i = 1; i <= n; ++i)
    for (long long j = 1; j <= m; ++j) read(a[i][j]);
  {
    std::vector<std::pair<long long, long long> > dr;
    for (long long i = 1; i <= n; ++i)
      for (long long j = 1; j <= m; ++j)
        dr.push_back(std::make_pair(a[i][j], i + j - 1));
    std::sort((dr).begin(), (dr).end());
    register long long cnt = 0;
    for (auto i : dr)
      if (!p[i.second]) p[i.second] = ++cnt;
    for (long long i = 1; i <= cnt; ++i) t[p[i]] = i;
    for (long long i = 1; i <= cnt; ++i) p[i] = t[i];
  }
  q = n + m - 1;
  register long long sum = 0;
  for (long long i = 1; i <= q; ++i) {
    b[p[i]] = 1;
    register long long t = calc();
    if (sum + t >= K) continue;
    b[p[i]] = -1;
    sum += t;
  }
  for (long long i = 1; i <= n; ++i, std::puts(""))
    for (long long j = 1; j <= m; ++j)
      std::putchar(b[i + j - 1] > 0 ? '(' : ')');
  return 0;
}
