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 MAX = 1e3 + 10;
const int INTMAX = ~(1 << 31);
const long long LLMAX = ~(1LL << 63);
int space[MAX][MAX];
int scalar(int *pt1, int *pt2) {
  int sum = 0;
  for (int i = 1; i <= 5; i++) {
    sum += pt1[i] * pt2[i];
  }
  return sum;
}
bool isGood(int *ptc, int *pt1, int *pt2) {
  int sum = 0;
  for (int i = 1; i <= 5; i++) {
    sum += (pt1[i] - ptc[i]) * (pt2[i] - ptc[i]);
  }
  if (sum <= 0) {
    return true;
  }
  return false;
}
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= 5; j++) {
      scanf("%d", &space[i][j]);
    }
  }
  vector<int> ans;
  for (int i = 1; i <= n; i++) {
    bool goodFlag = true;
    for (int j = 1; j <= n; j++) {
      if (j == i) {
        continue;
      }
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) {
          continue;
        }
        if (!isGood(space[i], space[j], space[k])) {
          goodFlag = false;
          break;
        }
      }
      if (!goodFlag) {
        break;
      }
    }
    if (goodFlag) {
      ans.push_back(i);
    }
  }
  cout << ans.size() << '\n';
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << '\n';
  }
}
