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 PI = (acos((long double)-1)) / 2;
struct Point {
  double a, b, c, d, e;
  Point operator-(Point B) {
    Point C;
    C.a = -(B.a - a);
    C.b = -(B.b - b);
    C.c = -(B.c - c);
    C.d = -(B.d - d);
    C.e = -(B.e - e);
    return C;
  }
};
double scalar(Point A, Point B) {
  return A.a * B.a + A.b * B.b + A.c * B.c + A.d * B.d + A.e * B.e;
}
double length(Point A) { return sqrt(scalar(A, A)); }
double ang(Point A, Point B, Point C) {
  Point AB = B - A;
  Point AC = C - A;
  double t = scalar(AB, AC);
  double s = t / (length(AB) * length(AC));
  return s;
}
int main() {
  int n;
  cin >> n;
  vector<Point> p(n);
  for (int i = 0; i < n; i++) {
    cin >> p[i].a >> p[i].b >> p[i].c >> p[i].d >> p[i].e;
  }
  bool q;
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    q = true;
    for (int j = 0; j < n; j++) {
      for (int t = j + 1; t < n; t++) {
        if (t != i && j != i && j != t) {
          if (ang(p[i], p[j], p[t]) > 0) {
            q = false;
            break;
          }
        }
        if (!q) break;
      }
      if (!q) break;
    }
    if (q) {
      ans.push_back(i + 1);
    }
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << endl;
  }
  return 0;
}
