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.
#include <bits/stdc++.h>
using namespace std;
struct point {
  long long a, b, c, d, e;
};
point arr[1010];
int n;
int ans[1010];
vector<int> v;
point get_v(point p, point q) {
  point ne;
  ne.a = q.a - p.a;
  ne.b = q.b - p.b;
  ne.c = q.c - p.c;
  ne.d = q.d - p.d;
  ne.e = q.e - p.e;
  return ne;
}
long long dot(point p, point q) {
  return (p.a * q.a) + (p.b * q.b) + (p.c * q.c) + (p.d * q.d) + (p.e * q.e);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++)
    scanf("%lld %lld %lld %lld %lld", &arr[i].a, &arr[i].b, &arr[i].c,
          &arr[i].d, &arr[i].e),
        ans[i] = 1;
  for (int i = 1; i <= n; i++) {
    if (ans[i]) {
      bool brk = false;
      for (int j = 1; j <= n; j++) {
        if (j == i) continue;
        for (int k = 1; k <= n; k++) {
          if (k == i || k == j) continue;
          point ab = get_v(arr[i], arr[j]);
          point ac = get_v(arr[i], arr[k]);
          long long res = dot(ab, ac);
          if (res == 0)
            continue;
          else if (res > 0) {
            ans[i] = 0;
            brk = true;
            break;
          }
        }
        if (brk) break;
      }
    }
  }
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (ans[i]) {
      cnt++;
      v.push_back(i);
    }
  }
  cout << cnt << endl;
  for (int i = 0; i < cnt; i++) {
    cout << v[i] << endl;
  }
  return 0;
}
