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;
const double eps = (double)1e-10;
struct point {
  vector<int> v;
  point() { v.clear(); }
  point(vector<int> _) {
    v.clear();
    for (int i = 0; i < _.size(); i++) v.push_back(_[i]);
  }
  bool operator<(const point& o) const { return v < o.v; }
};
vector<point> P;
int n;
point get_v(point a, point b) {
  point r;
  for (int i = 0; i < 5; i++) {
    r.v.push_back(b.v[i] - a.v[i]);
  }
  return r;
}
double get_up(point a, point b) {
  double r = 0.0;
  for (int i = 0; i < 5; i++) {
    r += a.v[i] * b.v[i];
  }
  return r;
}
double get_mod(point a, point b) {
  double r = 0.0;
  for (int i = 0; i < 5; i++) {
    r += (a.v[i] - b.v[i]) * (a.v[i] - b.v[i]);
  }
  return sqrt(r);
}
double get_angle(point a, point b, point c) {
  double up = get_up(get_v(a, b), get_v(a, c));
  double down = get_mod(a, b) * get_mod(a, c);
  return acos(up / down);
}
vector<int> ans;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a, b, c, d, e;
    cin >> a >> b >> c >> d >> e;
    P.push_back(point({a, b, c, d, e}));
  }
  for (int i = 0; i < n; i++) {
    bool good = true;
    for (int j = 0; j < n; j++) {
      if (i == j) continue;
      for (int k = j + 1; k < n; k++) {
        if (k == i) continue;
        double an = get_angle(P[i], P[j], P[k]);
        if (isnan(an)) {
          good = false;
          break;
        }
        an *= 180.0 / acos(-1.0);
        if (an + eps < 90.0) {
          good = false;
          break;
        }
      }
      if (!good) break;
    }
    if (good) ans.push_back(i + 1);
  }
  cout << ans.size() << '\n';
  for (int i = 0; i < ans.size(); i++) {
    printf("%d ", ans[i]);
  }
}
