#include <bits/stdc++.h>
using namespace std;
const int NMAX = 1e3 + 5;
struct point {
  int first, second, _3, _4, _5;
};
struct vec {
  int first, second, _3, _4, _5;
};
double sprod(vec &a, vec &b) {
  return a.first * b.first + a.second * b.second + a._3 * b._3 + a._4 * b._4 +
         a._5 * b._5;
}
bool is_acute(vec &a, vec &b) { return sprod(a, b) > 0; }
vec to_vec(point &a, point &b) {
  return {
      b.first - a.first, b.second - a.second, b._3 - a._3,
      b._4 - a._4,       b._5 - a._5,
  };
}
int n;
point ps[NMAX];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int first, second, _3, _4, _5;
    cin >> first >> second >> _3 >> _4 >> _5;
    ps[i] = {first, second, _3, _4, _5};
  }
  if (n > 33) {
    cout << 0;
  } else {
    vector<int> r;
    for (int i = 1; i <= n; i++) {
      bool is_good = true;
      for (int j = 1; j <= n - 1; j++) {
        for (int k = j + 1; k <= n; k++) {
          if (j != i && k != i) {
            point a = ps[i];
            point b = ps[j];
            point c = ps[k];
            vec ab = to_vec(a, b);
            vec ac = to_vec(a, c);
            if (is_acute(ab, ac)) {
              is_good = false;
            }
          }
        }
      }
      if (is_good) {
        r.push_back(i);
      }
    }
    cout << r.size() << endl;
    for (auto i : r) {
      cout << i << endl;
    }
  }
}

### Prompt

Please formulate a cpp solution to the following problem:

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;
const int NMAX = 1e3 + 5;
struct point {
  int first, second, _3, _4, _5;
};
struct vec {
  int first, second, _3, _4, _5;
};
double sprod(vec &a, vec &b) {
  return a.first * b.first + a.second * b.second + a._3 * b._3 + a._4 * b._4 +
         a._5 * b._5;
}
bool is_acute(vec &a, vec &b) { return sprod(a, b) > 0; }
vec to_vec(point &a, point &b) {
  return {
      b.first - a.first, b.second - a.second, b._3 - a._3,
      b._4 - a._4,       b._5 - a._5,
  };
}
int n;
point ps[NMAX];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int first, second, _3, _4, _5;
    cin >> first >> second >> _3 >> _4 >> _5;
    ps[i] = {first, second, _3, _4, _5};
  }
  if (n > 33) {
    cout << 0;
  } else {
    vector<int> r;
    for (int i = 1; i <= n; i++) {
      bool is_good = true;
      for (int j = 1; j <= n - 1; j++) {
        for (int k = j + 1; k <= n; k++) {
          if (j != i && k != i) {
            point a = ps[i];
            point b = ps[j];
            point c = ps[k];
            vec ab = to_vec(a, b);
            vec ac = to_vec(a, c);
            if (is_acute(ab, ac)) {
              is_good = false;
            }
          }
        }
      }
      if (is_good) {
        r.push_back(i);
      }
    }
    cout << r.size() << endl;
    for (auto i : r) {
      cout << i << endl;
    }
  }
}

```