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;
int n;
int points[11][5];
int main() {
  cin >> n;
  if (n > 11) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < 5; ++j) {
      cin >> points[i][j];
    }
  }
  int good[11];
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      for (int k = j + 1; k < n; ++k) {
        int ij[5];
        int ik[5];
        int kj[5];
        for (int l = 0; l < 5; ++l) {
          ij[l] = points[j][l] - points[i][l];
          ik[l] = points[k][l] - points[i][l];
          kj[l] = points[j][l] - points[k][l];
        }
        int pi = 0;
        int pj = 0;
        int pk = 0;
        int di = 0;
        int dj = 0;
        int dk = 0;
        for (int l = 0; l < 5; ++l) {
          pi += ij[l] * ik[l];
          pj += -ij[l] * -kj[l];
          pk += -ik[l] * kj[l];
        }
        if (pi > 0) good[i] = -3;
        if (pj > 0) good[j] = -3;
        if (pk > 0) good[k] = -3;
      }
    }
  }
  int count = 0;
  for (int i = 0; i < n; ++i) {
    if (good[i] != -3) ++count;
  }
  cout << count << endl;
  for (int i = 0; i < n; ++i) {
    if (good[i] != -3) cout << i + 1 << endl;
  }
  return 0;
}
