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 maxn = 1e3 + 666;
int n, p[maxn][6], len[maxn];
vector<int> rt;
int main(void) {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < 5; ++j) {
      scanf("%d", &p[i][j]);
      len[i] += p[i][j] * p[i][j];
    }
  }
  if (n > 12)
    cout << 0 << endl;
  else {
    for (int i = 0; i < n; ++i) {
      bool flag = true;
      for (int j = 0; j < n; ++j) {
        if (!flag) break;
        if (i == j) continue;
        for (int q = 0; q < min(16, n); ++q) {
          if (q == i || q == j) continue;
          int pt = 0;
          for (int k = 0; k < 5; ++k)
            pt += (p[q][k] - p[i][k]) * (p[j][k] - p[i][k]);
          if (pt > 0) {
            flag = false;
            break;
          }
        }
      }
      if (flag) rt.push_back(i + 1);
    }
    cout << rt.size() << endl;
    sort(rt.begin(), rt.end());
    for (auto t : rt) cout << t << endl;
  }
}
