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 int DIM = 5;
struct Point {
  Point(int a0 = 0, int a1 = 0, int a2 = 0, int a3 = 0, int a4 = 0) {
    c[0] = a0;
    c[1] = a1;
    c[2] = a2;
    c[3] = a3;
    c[4] = a4;
  }
  int c[DIM];
};
unsigned long long scalar(const Point& a, const Point& b) {
  return a.c[0] * b.c[0] + a.c[1] * b.c[1] + a.c[2] * b.c[2] + a.c[3] * b.c[3] +
         a.c[4] * b.c[4];
}
Point vec(const Point& a, const Point& b) {
  return Point(b.c[0] - a.c[0], b.c[1] - a.c[1], b.c[2] - a.c[2],
               b.c[3] - a.c[3], b.c[4] - a.c[4]);
}
vector<Point> p;
int main() {
  int n;
  cin >> n;
  p.resize(n);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < DIM; ++j) scanf("%d", &p[i].c[j]);
  vector<int> ans;
  for (int a = 0; a < n; ++a) {
    bool bad = false;
    for (int b = 0; b < n; ++b) {
      if (a == b) continue;
      Point ab = vec(p[a], p[b]);
      for (int c = 0; c < n; ++c) {
        if (b == c || a == c) continue;
        Point ac = vec(p[a], p[c]);
        int sc = scalar(ab, ac);
        if (sc > 0) {
          bad = true;
          b = n;
          break;
        }
      }
    }
    if (!bad) ans.push_back(a);
  }
  cout << ans.size() << "\n";
  for (auto elem : ans) cout << elem + 1 << endl;
}
