#include <bits/stdc++.h>
using namespace std;
long long dx[4] = {1, 0, -1, 0};
long long dy[4] = {0, -1, 0, 1};
template <class T>
void inputVector(vector<T> &v, long long n) {
  v.resize(n);
  for (long long i = 0; i < v.size(); i++) cin >> v[i];
}
struct Point {
  long long p[5];
  Point() {}
  Point(long long a, long long b, long long c, long long d, long long e) {
    p[0] = a;
    p[1] = b;
    p[2] = c;
    p[3] = d;
    p[4] = e;
  }
};
struct Vector {
  long long p[5];
  Vector() {}
  Vector(long long a, long long b, long long c, long long d, long long e) {
    p[0] = a;
    p[1] = b;
    p[2] = c;
    p[3] = d;
    p[4] = e;
  }
  Vector(Point &a, Point &b) {
    for (long long i = 0; i < (5); i++) {
      p[i] = b.p[i] - a.p[i];
    }
  }
  double norm() {
    double ret = 0;
    for (long long i = 0; i < (5); i++) ret += p[i] * p[i];
    return sqrt(ret);
  }
};
double calcAngle(Point &a, Point &b, Point &c) {
  Vector v1 = Vector(b, a);
  Vector v2 = Vector(c, a);
  double ret = 0;
  for (long long i = 0; i < (5); i++) ret += v1.p[i] * v2.p[i];
  ret /= v1.norm();
  ret /= v2.norm();
  return acos(ret);
}
signed main() {
  long long n;
  cin >> n;
  vector<Point> points;
  for (long long i = 0; i < (n); i++) {
    long long a, b, c, d, e;
    cin >> a >> b >> c >> d >> e;
    points.push_back(Point(a, b, c, d, e));
  }
  vector<long long> ret;
  for (long long i = 0; i < (n); i++) {
    bool flag = true;
    for (long long j = 0; j < (n); j++) {
      if (i == j) continue;
      for (long long k = 0; k < (n); k++) {
        if (k == i || k == j) continue;
        double angle = calcAngle(points[i], points[j], points[k]);
        if (angle < acos(-1) / 2 - 0.00000001) {
          flag = false;
          break;
        }
      }
      if (!flag) break;
    }
    if (flag) {
      ret.push_back(i + 1);
    }
  }
  cout << ret.size() << endl;
  for (long long i = 0; i < (ret.size()); i++) {
    cout << ret[i] << endl;
  }
  return 0;
}

### Prompt

Generate 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;
long long dx[4] = {1, 0, -1, 0};
long long dy[4] = {0, -1, 0, 1};
template <class T>
void inputVector(vector<T> &v, long long n) {
  v.resize(n);
  for (long long i = 0; i < v.size(); i++) cin >> v[i];
}
struct Point {
  long long p[5];
  Point() {}
  Point(long long a, long long b, long long c, long long d, long long e) {
    p[0] = a;
    p[1] = b;
    p[2] = c;
    p[3] = d;
    p[4] = e;
  }
};
struct Vector {
  long long p[5];
  Vector() {}
  Vector(long long a, long long b, long long c, long long d, long long e) {
    p[0] = a;
    p[1] = b;
    p[2] = c;
    p[3] = d;
    p[4] = e;
  }
  Vector(Point &a, Point &b) {
    for (long long i = 0; i < (5); i++) {
      p[i] = b.p[i] - a.p[i];
    }
  }
  double norm() {
    double ret = 0;
    for (long long i = 0; i < (5); i++) ret += p[i] * p[i];
    return sqrt(ret);
  }
};
double calcAngle(Point &a, Point &b, Point &c) {
  Vector v1 = Vector(b, a);
  Vector v2 = Vector(c, a);
  double ret = 0;
  for (long long i = 0; i < (5); i++) ret += v1.p[i] * v2.p[i];
  ret /= v1.norm();
  ret /= v2.norm();
  return acos(ret);
}
signed main() {
  long long n;
  cin >> n;
  vector<Point> points;
  for (long long i = 0; i < (n); i++) {
    long long a, b, c, d, e;
    cin >> a >> b >> c >> d >> e;
    points.push_back(Point(a, b, c, d, e));
  }
  vector<long long> ret;
  for (long long i = 0; i < (n); i++) {
    bool flag = true;
    for (long long j = 0; j < (n); j++) {
      if (i == j) continue;
      for (long long k = 0; k < (n); k++) {
        if (k == i || k == j) continue;
        double angle = calcAngle(points[i], points[j], points[k]);
        if (angle < acos(-1) / 2 - 0.00000001) {
          flag = false;
          break;
        }
      }
      if (!flag) break;
    }
    if (flag) {
      ret.push_back(i + 1);
    }
  }
  cout << ret.size() << endl;
  for (long long i = 0; i < (ret.size()); i++) {
    cout << ret[i] << endl;
  }
  return 0;
}

```