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;
double PI2 = 1.57079632679;
struct Point {
  long long x[5];
  void read() {
    for (int i(0); i < 5; i++) cin >> x[i];
  }
};
Point operator-(Point a, Point b) {
  Point c;
  for (int i(0); i < 5; i++) c.x[i] = a.x[i] - b.x[i];
  return c;
}
long long operator*(Point a, Point b) {
  long long r = 0;
  for (int i(0); i < 5; i++) r += a.x[i] * b.x[i];
  return r;
}
double len(Point p) { return sqrt(p * p); }
double angle(Point a, Point b, Point c) {
  Point v1 = b - a;
  Point v2 = c - a;
  return acos(v1 * v2 / (len(v1) * len(v2)));
}
vector<pair<Point, int> > p;
vector<int> ans;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  for (int i(0); i < n; i++) {
    Point pnt;
    pnt.read();
    p.push_back({pnt, i});
  }
  random_shuffle(p.begin(), p.end());
  for (int i(0); i < n; i++) {
    bool flag = true;
    for (int j(0); j < n; j++) {
      if (j == i) continue;
      for (int k(0); k < n; k++) {
        if (k == j || k == i) continue;
        if (angle(p[i].first, p[j].first, p[k].first) - PI2 <= -1e-9) {
          flag = false;
          break;
        }
      }
      if (!flag) break;
    }
    if (flag) ans.push_back(p[i].second);
  }
  cout << ans.size() << "\n";
  for (auto i : ans) cout << i + 1 << " ";
  return 0;
}
