#include <bits/stdc++.h>
using namespace std;
struct Point {
  int a, b, c, d, e;
  Point() { a = b = c = d = e = 0; }
  Point(int aa, int bb, int cc, int dd, int ee) {
    a = aa;
    b = bb;
    c = cc;
    d = dd;
    e = ee;
  }
};
Point difference(Point s, Point t) {
  return Point(s.a - t.a, s.b - t.b, s.c - t.c, s.d - t.d, s.e - t.e);
}
int dot(Point s, Point t) {
  return (s.a * t.a + s.b * t.b + s.c * t.c + s.d * t.d + s.e * t.e);
}
Point x[34];
vector<Point> v;
vector<int> ans;
bool flag;
int main() {
  int N;
  cin >> N;
  if (N >= 34) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 1; i <= N; i++) {
    cin >> x[i].a >> x[i].b >> x[i].c >> x[i].d >> x[i].e;
  }
  for (int i = 1; i <= N; i++) {
    v.clear();
    flag = true;
    for (int j = 1; j <= N; j++) {
      if (j != i) {
        v.push_back(difference(x[j], x[i]));
      }
    }
    for (int j = 0; j < N - 1; j++) {
      for (int k = 0; k < N - 1; k++) {
        if (k != j && dot(v[j], v[k]) > 0) {
          flag = false;
        }
      }
    }
    if (flag) {
      ans.push_back(i);
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << endl;
  }
}

### Prompt

Create a solution in Cpp for 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;
struct Point {
  int a, b, c, d, e;
  Point() { a = b = c = d = e = 0; }
  Point(int aa, int bb, int cc, int dd, int ee) {
    a = aa;
    b = bb;
    c = cc;
    d = dd;
    e = ee;
  }
};
Point difference(Point s, Point t) {
  return Point(s.a - t.a, s.b - t.b, s.c - t.c, s.d - t.d, s.e - t.e);
}
int dot(Point s, Point t) {
  return (s.a * t.a + s.b * t.b + s.c * t.c + s.d * t.d + s.e * t.e);
}
Point x[34];
vector<Point> v;
vector<int> ans;
bool flag;
int main() {
  int N;
  cin >> N;
  if (N >= 34) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 1; i <= N; i++) {
    cin >> x[i].a >> x[i].b >> x[i].c >> x[i].d >> x[i].e;
  }
  for (int i = 1; i <= N; i++) {
    v.clear();
    flag = true;
    for (int j = 1; j <= N; j++) {
      if (j != i) {
        v.push_back(difference(x[j], x[i]));
      }
    }
    for (int j = 0; j < N - 1; j++) {
      for (int k = 0; k < N - 1; k++) {
        if (k != j && dot(v[j], v[k]) > 0) {
          flag = false;
        }
      }
    }
    if (flag) {
      ans.push_back(i);
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << endl;
  }
}

```