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 ans[1003], siz = 0, points[33] = {0};
struct node {
  int data[5];
  int index;
} nodes[1003];
bool check(int index, int n) {
  int i, j, k, dot;
  for (i = 0; i < n; i++) {
    if (i == index) {
      continue;
    }
    for (j = 0; j < n; j++) {
      if (i == j || j == index) {
        continue;
      }
      dot = 0;
      for (k = 0; k < 5; k++) {
        dot += ((nodes[i].data[k] - nodes[index].data[k]) *
                (nodes[j].data[k] - nodes[index].data[k]));
      }
      if (dot > 0) {
        return false;
      }
    }
  }
  return true;
}
int main() {
  int n, i, j, k;
  cin >> n;
  for (i = 0; i < n; i++) {
    for (j = 0; j < 5; j++) {
      cin >> nodes[i].data[j];
    }
  }
  bool good;
  for (i = 0; i < n; i++) {
    for (j = 0; j < 33; j++) {
      points[j] = 0;
    }
    good = true;
    if (n > 100) {
      for (j = 0; j < n; j++) {
        if (i == j) {
          continue;
        }
        int index = 0, add = 1;
        for (k = 0; k < 5; k++) {
          int v = nodes[j].data[k] - nodes[i].data[k];
          if (v > 0) {
            index += add;
          }
          add *= 2;
        }
        points[index] += 1;
        if (points[index] >= 2) {
          good = false;
          break;
        }
      }
    }
    if (good) {
      if (check(i, n)) {
        ans[siz] = i + 1;
        siz++;
      }
    }
  }
  cout << siz << "\n";
  for (i = 0; i < siz; i++) {
    cout << ans[i] << "\n";
  }
  return 0;
}
