#include <bits/stdc++.h>
using namespace std;
double PI = acos(-1);
double EPS = 1e-9;
struct Point {
  int a;
  int b;
  int c;
  int d;
  int e;
  bool operator<(Point other) const {
    if (a == other.a) {
      if (b == other.b) {
        if (c == other.c) {
          if (d == other.d) {
            return e < other.e;
          }
          return d < other.d;
        }
        return c < other.c;
      }
      return b < other.b;
    }
    return a < other.a;
  }
  Point operator-(Point other) const {
    return (Point){a - other.a, b - other.b, c - other.c, d - other.d,
                   e - other.e};
  }
  int det(Point other) {
    return a * other.a + b * other.b + c * other.c + d * other.d + e * other.e;
  }
  int det() { return det(*this); }
  void read() { scanf("%d %d %d %d %d", &a, &b, &c, &d, &e); }
};
Point arr[1005];
bool done[1005];
int n;
void read() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) arr[i].read();
}
void solve() {
  vector<int> ret;
  for (int i = 0; i < n; i++) {
    if (done[i]) {
      continue;
    }
    vector<pair<int, Point>> v;
    for (int j = 0; j < n; j++)
      if (j != i) v.push_back({j, arr[j]});
    bool bad = false;
    for (int j = 0; j < v.size() && !bad; j++)
      for (int k = j + 1; k < v.size() && !bad; k++) {
        Point a = v[j].second - arr[i];
        Point b = v[k].second - arr[i];
        double atas = a.det(b);
        double bawah = 1ll * a.det() * b.det();
        bawah = sqrt(bawah);
        double ang = acos(atas / bawah);
        ang = ang / PI * 180;
        while (ang < 0) ang += 180;
        while (ang > 180) ang -= 180;
        if (ang + EPS < 90) {
          bad = true;
        } else {
          done[v[j].first] = true;
          done[v[k].first] = true;
        }
      }
    if (!bad) {
      ret.push_back(i + 1);
    }
  }
  cout << ret.size() << endl;
  for (int x : ret) cout << x << endl;
}
int main() {
  read();
  solve();
  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;
double PI = acos(-1);
double EPS = 1e-9;
struct Point {
  int a;
  int b;
  int c;
  int d;
  int e;
  bool operator<(Point other) const {
    if (a == other.a) {
      if (b == other.b) {
        if (c == other.c) {
          if (d == other.d) {
            return e < other.e;
          }
          return d < other.d;
        }
        return c < other.c;
      }
      return b < other.b;
    }
    return a < other.a;
  }
  Point operator-(Point other) const {
    return (Point){a - other.a, b - other.b, c - other.c, d - other.d,
                   e - other.e};
  }
  int det(Point other) {
    return a * other.a + b * other.b + c * other.c + d * other.d + e * other.e;
  }
  int det() { return det(*this); }
  void read() { scanf("%d %d %d %d %d", &a, &b, &c, &d, &e); }
};
Point arr[1005];
bool done[1005];
int n;
void read() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) arr[i].read();
}
void solve() {
  vector<int> ret;
  for (int i = 0; i < n; i++) {
    if (done[i]) {
      continue;
    }
    vector<pair<int, Point>> v;
    for (int j = 0; j < n; j++)
      if (j != i) v.push_back({j, arr[j]});
    bool bad = false;
    for (int j = 0; j < v.size() && !bad; j++)
      for (int k = j + 1; k < v.size() && !bad; k++) {
        Point a = v[j].second - arr[i];
        Point b = v[k].second - arr[i];
        double atas = a.det(b);
        double bawah = 1ll * a.det() * b.det();
        bawah = sqrt(bawah);
        double ang = acos(atas / bawah);
        ang = ang / PI * 180;
        while (ang < 0) ang += 180;
        while (ang > 180) ang -= 180;
        if (ang + EPS < 90) {
          bad = true;
        } else {
          done[v[j].first] = true;
          done[v[k].first] = true;
        }
      }
    if (!bad) {
      ret.push_back(i + 1);
    }
  }
  cout << ret.size() << endl;
  for (int x : ret) cout << x << endl;
}
int main() {
  read();
  solve();
  return 0;
}

```