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 {
  int p[5];
  int &operator[](int i) { return p[i]; }
};
point operator-(point &l, point &r) {
  point ans;
  for (int i = 0; i < 5; i++) ans[i] = r[i] - l[i];
  return ans;
}
point p[1010];
double dot(point &l, point &r) {
  double ans = 0;
  for (int i = 0; i < 5; i++) ans += 1.0 * l[i] * r[i];
  return ans;
}
double length(point &i) { return sqrt(dot(i, i)); }
double ang(point &l, point &r) {
  return acos(dot(l, r) / (length(l) * length(r)));
}
double max_theta = acos(-1.0) / 2.0;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 5; j++) cin >> p[i][j];
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    bool good = true;
    for (int j = 0; j < n && good; j++) {
      if (i == j) continue;
      for (int k = 0; k < n && good; k++) {
        if (i == k || j == k) continue;
        point ij = p[j] - p[i];
        point ik = p[k] - p[i];
        double theta = ang(ij, ik);
        good &= theta >= max_theta;
      }
    }
    if (good) ans.push_back(i + 1);
  }
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) cout << ans[i] << endl;
  return 0;
}
