#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct outputer;
struct outputable {};
template <typename T>
inline auto sqr(T x) -> decltype(x * x) {
  return x * x;
}
template <typename T1, typename T2>
inline bool umx(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T1, typename T2>
inline bool umn(T1& a, T2 b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
const int N = 1000;
const int M = 5;
struct Input {
  int n;
  int a[N][M];
  bool read() {
    if (!(cin >> n)) {
      return 0;
    }
    for (int i = int(0); i < int(n); ++i) {
      for (int j = int(0); j < int(M); ++j) {
        scanf("%d", &a[i][j]);
      }
    }
    return 1;
  }
  void init(const Input& input) { *this = input; }
};
struct Data : Input {
  vector<int> ans;
  void write() {
    cout << ((int)(ans).size()) << endl;
    for (int i = int(0); i < int(((int)(ans).size())); ++i) {
      cout << ans[i] + 1 << endl;
    }
  }
};
namespace Main {
struct Solution : Data {
  void solve() {
    if (n > 100) {
      return;
    }
    for (int i = int(0); i < int(n); ++i) {
      bool ok = 1;
      for (int j = int(0); j < int(n); ++j) {
        if (j != i) {
          for (int k = int(0); k < int(j); ++k) {
            if (k != i) {
              int s = 0;
              for (int t = int(0); t < int(M); ++t) {
                s += (a[j][t] - a[i][t]) * (a[k][t] - a[i][t]);
              }
              if (s > 0) {
                ok = 0;
              }
            }
          }
        }
      }
      if (ok) {
        ans.emplace_back(i);
      }
    }
  }
  void clear() { *this = Solution(); }
};
}  // namespace Main
Main::Solution sol;
int main() {
  cout.setf(ios::showpoint | ios::fixed);
  cout.precision(20);
  sol.read();
  sol.solve();
  sol.write();
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.

We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors <image> and <image> is acute (i.e. strictly less than <image>). Otherwise, the point is called good.

The angle between vectors <image> and <image> in 5-dimensional space is defined as <image>, where <image> is the scalar product and <image> is length of <image>.

Given the list of points, print the indices of the good points in ascending order.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.

The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.

Output

First, print a single integer k — the number of good points.

Then, print k integers, each on their own line — the indices of the good points in ascending order.

Examples

Input

6
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1


Output

1
1


Input

3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0


Output

0

Note

In the first sample, the first point forms exactly a <image> angle with all other pairs of points, so it is good.

In the second sample, along the cd plane, we can see the points look as follows:

<image>

We can see that all angles here are acute, so no points are good.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct outputer;
struct outputable {};
template <typename T>
inline auto sqr(T x) -> decltype(x * x) {
  return x * x;
}
template <typename T1, typename T2>
inline bool umx(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T1, typename T2>
inline bool umn(T1& a, T2 b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
const int N = 1000;
const int M = 5;
struct Input {
  int n;
  int a[N][M];
  bool read() {
    if (!(cin >> n)) {
      return 0;
    }
    for (int i = int(0); i < int(n); ++i) {
      for (int j = int(0); j < int(M); ++j) {
        scanf("%d", &a[i][j]);
      }
    }
    return 1;
  }
  void init(const Input& input) { *this = input; }
};
struct Data : Input {
  vector<int> ans;
  void write() {
    cout << ((int)(ans).size()) << endl;
    for (int i = int(0); i < int(((int)(ans).size())); ++i) {
      cout << ans[i] + 1 << endl;
    }
  }
};
namespace Main {
struct Solution : Data {
  void solve() {
    if (n > 100) {
      return;
    }
    for (int i = int(0); i < int(n); ++i) {
      bool ok = 1;
      for (int j = int(0); j < int(n); ++j) {
        if (j != i) {
          for (int k = int(0); k < int(j); ++k) {
            if (k != i) {
              int s = 0;
              for (int t = int(0); t < int(M); ++t) {
                s += (a[j][t] - a[i][t]) * (a[k][t] - a[i][t]);
              }
              if (s > 0) {
                ok = 0;
              }
            }
          }
        }
      }
      if (ok) {
        ans.emplace_back(i);
      }
    }
  }
  void clear() { *this = Solution(); }
};
}  // namespace Main
Main::Solution sol;
int main() {
  cout.setf(ios::showpoint | ios::fixed);
  cout.precision(20);
  sol.read();
  sol.solve();
  sol.write();
  return 0;
}

```