#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
inline void gn(long long &first) {
  int sg = 1;
  char c;
  while (((c = getchar()) < '0' || c > '9') && c != '-')
    ;
  c == '-' ? (sg = -1, first = 0) : (first = c - '0');
  while ((c = getchar()) >= '0' && c <= '9') first = first * 10 + c - '0';
  first *= sg;
}
inline void gn(int &first) {
  long long t;
  gn(t);
  first = t;
}
inline void gn(unsigned long long &first) {
  long long t;
  gn(t);
  first = t;
}
inline void gn(double &first) {
  double t;
  scanf("%lf", &t);
  first = t;
}
inline void gn(long double &first) {
  double t;
  scanf("%lf", &t);
  first = t;
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
struct point {
  long long a, b, c, d, e;
  point(long long a = 0, long long b = 0, long long c = 0, long long d = 0,
        long long e = 0)
      : a(a), b(b), c(c), d(d), e(e) {}
  point operator-(point p) {
    return point(a - p.a, b - p.b, c - p.c, d - p.d, e - p.e);
  }
  void input() { gn(a), gn(b), gn(c), gn(d), gn(e); }
  void print() {
    cout << a << ' ' << b << ' ' << c << ' ' << d << ' ' << e << endl;
  }
  double nor() {
    return sqrt((double)(((a) * (a)) + ((b) * (b)) + ((c) * (c)) + ((d) * (d)) +
                         ((e) * (e))));
  }
} p[1010], c, q[1010];
double dot(point first, point second) {
  return (double)(first.a * second.a + first.b * second.b + first.c * second.c +
                  first.d * second.d + first.e * second.e);
}
double angle(point a, point b) {
  double ans = dot(a, b) / a.nor() / b.nor();
  smin(ans, 1.), smax(ans, -1.);
  return acos(ans);
}
int flag[1010];
double angle(point a, point b, point c) { return angle(a - c, b - c); }
int main() {
  int n;
  gn(n);
  for (int i = 0; i < n; i++) p[i].input();
  if (n > 30) return puts("0"), 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (j == i) continue;
      for (int k = 0; k < n; k++) {
        if (i == k || j == k) continue;
        double al = angle(p[j], p[k], p[i]);
        if (al > acos(-1) / 2. - 1e-8) continue;
        flag[i] = 1;
        break;
      }
      if (flag[i]) break;
    }
  }
  int num = 0;
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    num++;
  }
  printf("%d\n", num);
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    printf("%d ", i + 1);
  }
  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;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
inline void gn(long long &first) {
  int sg = 1;
  char c;
  while (((c = getchar()) < '0' || c > '9') && c != '-')
    ;
  c == '-' ? (sg = -1, first = 0) : (first = c - '0');
  while ((c = getchar()) >= '0' && c <= '9') first = first * 10 + c - '0';
  first *= sg;
}
inline void gn(int &first) {
  long long t;
  gn(t);
  first = t;
}
inline void gn(unsigned long long &first) {
  long long t;
  gn(t);
  first = t;
}
inline void gn(double &first) {
  double t;
  scanf("%lf", &t);
  first = t;
}
inline void gn(long double &first) {
  double t;
  scanf("%lf", &t);
  first = t;
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
struct point {
  long long a, b, c, d, e;
  point(long long a = 0, long long b = 0, long long c = 0, long long d = 0,
        long long e = 0)
      : a(a), b(b), c(c), d(d), e(e) {}
  point operator-(point p) {
    return point(a - p.a, b - p.b, c - p.c, d - p.d, e - p.e);
  }
  void input() { gn(a), gn(b), gn(c), gn(d), gn(e); }
  void print() {
    cout << a << ' ' << b << ' ' << c << ' ' << d << ' ' << e << endl;
  }
  double nor() {
    return sqrt((double)(((a) * (a)) + ((b) * (b)) + ((c) * (c)) + ((d) * (d)) +
                         ((e) * (e))));
  }
} p[1010], c, q[1010];
double dot(point first, point second) {
  return (double)(first.a * second.a + first.b * second.b + first.c * second.c +
                  first.d * second.d + first.e * second.e);
}
double angle(point a, point b) {
  double ans = dot(a, b) / a.nor() / b.nor();
  smin(ans, 1.), smax(ans, -1.);
  return acos(ans);
}
int flag[1010];
double angle(point a, point b, point c) { return angle(a - c, b - c); }
int main() {
  int n;
  gn(n);
  for (int i = 0; i < n; i++) p[i].input();
  if (n > 30) return puts("0"), 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (j == i) continue;
      for (int k = 0; k < n; k++) {
        if (i == k || j == k) continue;
        double al = angle(p[j], p[k], p[i]);
        if (al > acos(-1) / 2. - 1e-8) continue;
        flag[i] = 1;
        break;
      }
      if (flag[i]) break;
    }
  }
  int num = 0;
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    num++;
  }
  printf("%d\n", num);
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    printf("%d ", i + 1);
  }
  return 0;
}

```