#include <bits/stdc++.h>
using namespace std;
const int maxN = 1e3 + 9;
const long long INF = 1e18 + 9;
struct point {
  long long a, b, c, d, e;
  point(long long a, long long b, long long c, long long d, long long e)
      : a(a), b(b), c(c), d(d), e(e) {}
  point() : a(0), b(0), c(0), d(0), e(0) {}
};
point operator+(point a, point b) {
  return point(a.a + b.a, a.b + b.b, a.c + b.c, a.d + b.d, a.e + b.e);
}
point operator-(point a, point b) {
  return point(a.a - b.a, a.b - b.b, a.c - b.c, a.d - b.d, a.e - b.e);
}
point operator*(point a, int k) {
  return point(a.a * k, a.b * k, a.c * k, a.d * k, a.e * k);
}
long long get(point a) {
  return a.a * a.a + a.b * a.b + a.c * a.c + a.d * a.d + a.e * a.e;
}
point c[maxN];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld%lld%lld%lld", &c[i].a, &c[i].b, &c[i].c, &c[i].d, &c[i].e);
  }
  if (n == 1) {
    cout << 1 << endl << 1;
    return 0;
  }
  if (n == 2) {
    cout << 2 << endl << 1 << ' ' << 2;
    return 0;
  }
  long long dist = INF;
  int a = -1, b = -1;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      point that = c[i] - c[j];
      long long now = get(that);
      if (now <= dist) {
        dist = now;
        a = i;
        b = j;
      }
    }
  }
  bool is_a = true, is_b = true;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      point center = c[i] + c[j];
      long long current = get(c[i] - c[j]);
      if (i != a && j != a) {
        point fst = c[a] * 2;
        long long need = get(fst - center);
        if (need > current) {
          is_a = false;
        }
      }
      if (i != b && j != b) {
        point snd = c[b] * 2;
        long long need = get(snd - center);
        if (need > current) {
          is_b = false;
        }
      }
    }
  }
  if (is_a) {
    cout << 1 << endl << a + 1;
    return 0;
  }
  if (is_b) {
    cout << 1 << endl << b + 1;
    return 0;
  }
  cout << 0;
  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;
const int maxN = 1e3 + 9;
const long long INF = 1e18 + 9;
struct point {
  long long a, b, c, d, e;
  point(long long a, long long b, long long c, long long d, long long e)
      : a(a), b(b), c(c), d(d), e(e) {}
  point() : a(0), b(0), c(0), d(0), e(0) {}
};
point operator+(point a, point b) {
  return point(a.a + b.a, a.b + b.b, a.c + b.c, a.d + b.d, a.e + b.e);
}
point operator-(point a, point b) {
  return point(a.a - b.a, a.b - b.b, a.c - b.c, a.d - b.d, a.e - b.e);
}
point operator*(point a, int k) {
  return point(a.a * k, a.b * k, a.c * k, a.d * k, a.e * k);
}
long long get(point a) {
  return a.a * a.a + a.b * a.b + a.c * a.c + a.d * a.d + a.e * a.e;
}
point c[maxN];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld%lld%lld%lld", &c[i].a, &c[i].b, &c[i].c, &c[i].d, &c[i].e);
  }
  if (n == 1) {
    cout << 1 << endl << 1;
    return 0;
  }
  if (n == 2) {
    cout << 2 << endl << 1 << ' ' << 2;
    return 0;
  }
  long long dist = INF;
  int a = -1, b = -1;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      point that = c[i] - c[j];
      long long now = get(that);
      if (now <= dist) {
        dist = now;
        a = i;
        b = j;
      }
    }
  }
  bool is_a = true, is_b = true;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      point center = c[i] + c[j];
      long long current = get(c[i] - c[j]);
      if (i != a && j != a) {
        point fst = c[a] * 2;
        long long need = get(fst - center);
        if (need > current) {
          is_a = false;
        }
      }
      if (i != b && j != b) {
        point snd = c[b] * 2;
        long long need = get(snd - center);
        if (need > current) {
          is_b = false;
        }
      }
    }
  }
  if (is_a) {
    cout << 1 << endl << a + 1;
    return 0;
  }
  if (is_b) {
    cout << 1 << endl << b + 1;
    return 0;
  }
  cout << 0;
  return 0;
}

```