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;
inline void out(int a) { printf("%d\n", a); }
inline void out(int a, int b) { printf("%d %d\n", a, b); }
inline void outf(double a) { printf("%3.lf\n", a); }
inline void outf(double a, double b) { printf("%3.lf %3.lf\n", a, b); }
inline void base() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
}
vector<vector<long long> > ls;
double angle(vector<long long> a, vector<long long> b, vector<long long> c) {
  double lena, lenb;
  lena = lenb = 0;
  double scal = 0;
  for (int(i) = 0; (i) < (5); (i)++) {
    double x = (b[i] - a[i]);
    double y = (c[i] - a[i]);
    scal += x * y;
    lena += x * x;
    lenb += y * y;
  }
  lena = sqrt(lena);
  lenb = sqrt(lenb);
  return atan2(scal, lena * lenb);
}
vector<long long> pus;
bool cmp(vector<long long> b, vector<long long> c) {
  double ang = angle(pus, b, c);
  return ang < 180.0;
}
int main() {
  base();
  int n;
  cin >> n;
  for (int(i) = 0; (i) < (n); (i)++) {
    vector<long long> tmp;
    for (int(i) = 0; (i) < (5); (i)++) {
      long long a;
      cin >> a;
      tmp.push_back(a);
    }
    ls.push_back(tmp);
  }
  long long ans = 0;
  vector<long long> out;
  for (int(i) = 0; (i) < (n); (i)++) {
    bool good = true;
    for (int(j) = 0; (j) < (n); (j)++) {
      if (i == j) continue;
      for (int(k) = 0; (k) < (n); (k)++) {
        if (k == i || k == j) continue;
        if (angle(ls[i], ls[j], ls[k]) > 0.0) {
          good = false;
          break;
        }
      }
      if (!good) break;
    }
    if (good) ans++, out.push_back(i + 1);
  }
  cout << ans << endl;
  for (int(i) = 0; (i) < (ans); (i)++) {
    cout << out[i] << endl;
  }
  return 0;
}
