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 point5d {
  int c[5];
  friend istream& operator>>(istream& in, point5d& p) {
    for (int i = 0; i < 5; i++) in >> p.c[i];
    return in;
  }
  int inner(const point5d& p1, const point5d& p2) {
    int res = 0;
    for (int i = 0; i < 5; i++) res += (p1.c[i] - c[i]) * (p2.c[i] - c[i]);
    return res;
  }
};
bool isgoodpoint(int i, vector<point5d>& vp, int n) {
  for (int j = 0; j < n; j++) {
    for (int k = j + 1; k < n; k++) {
      if (i != j && i != k && vp[i].inner(vp[j], vp[k]) > 0) return false;
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  vector<point5d> vp(n);
  for (int i = 0; i < n; i++) cin >> vp[i];
  vector<bool> isgood(n);
  int count = 0;
  for (int i = 0; i < n; i++) {
    isgood[i] = isgoodpoint(i, vp, n);
    if (isgood[i]) count++;
  }
  cout << count << '\n';
  for (int i = 0; i < n; i++)
    if (isgood[i]) cout << (i + 1) << '\n';
}
