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>
int main() {
  std::ios_base::sync_with_stdio(false);
  int n;
  std::vector<std::array<int, 5>> dots;
  std::cin >> n;
  dots.reserve(n);
  for (int i = 0; i < n; i++) {
    std::array<int, 5> dot;
    for (int j = 0; j < 5; j++) {
      std::cin >> dot[j];
    }
    dots.push_back(dot);
  }
  std::vector<int> good_points;
  good_points.reserve(n);
  for (int i = 0; i < n; i++) {
    bool bad_dot = false;
    for (int j = 0; j < n; j++) {
      if (i != j) {
        for (int k = j + 1; k < n; k++) {
          if (i != k && j != k) {
            long long mult = 0;
            for (int coord = 0; coord < 5; coord++) {
              mult += (dots[j][coord] - dots[i][coord]) *
                      (dots[k][coord] - dots[i][coord]);
            }
            if (mult > 0) {
              bad_dot = true;
              break;
            }
          }
        }
        if (bad_dot) {
          break;
        }
      }
    }
    if (!bad_dot) {
      good_points.push_back(i);
    }
  }
  std::cout << good_points.size() << std::endl;
  for (auto& index : good_points) {
    std::cout << index + 1 << std::endl;
  }
  return 0;
}
