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 {
  vector<double> coords = vector<double>(5);
};
struct vec {
  vector<double> coords = vector<double>(5);
  double length;
};
int main() {
  int n;
  cin >> n;
  vector<point> points(n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < 5; j++) cin >> points[i].coords[j];
  bool ans[n];
  for (int i = 0; i < n; i++) ans[i] = true;
  int k_good = n;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = j + 1; k < n; k++) {
        if (i != j && i != k && j != k && ans[i]) {
          vec vecij;
          vec vecik;
          double sum_forl1 = 0;
          double sum_forl2 = 0;
          double vec_pow = 0;
          for (int n = 0; n < 5; n++) {
            vecij.coords[n] = points[j].coords[n] - points[i].coords[n];
            vecik.coords[n] = points[k].coords[n] - points[i].coords[n];
            sum_forl1 += vecij.coords[n] * vecij.coords[n];
            sum_forl2 += vecik.coords[n] * vecik.coords[n];
            vec_pow += vecik.coords[n] * vecij.coords[n];
          }
          vec_pow = sqrt(vec_pow);
          vecij.length = sqrt(sum_forl1);
          vecik.length = sqrt(sum_forl2);
          if (acos(vec_pow / (vecij.length * vecik.length)) * 180 / 3.14159265 <
              90) {
            ans[i] = false;
            k_good--;
          } else
            ans[i] = true;
        }
      }
  cout << k_good << '\n';
  for (int i = 0; i < n; i++)
    if (ans[i]) cout << i + 1 << '\n';
}
