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 = 1005;
struct node {
  int a, b, c, d, e;
} nodes[maxn];
bool vis[maxn];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    scanf("%d%d%d%d%d", &nodes[i].a, &nodes[i].b, &nodes[i].c, &nodes[i].d,
          &nodes[i].e);
  }
  long long temp;
  int cnt = 0;
  int ans[maxn];
  for (int i = 1; i <= n; i++)
    if (!vis[i]) {
      bool flag = true;
      for (int j = 1; j <= n; j++)
        if (j != i)
          for (int k = 1; k <= n; k++)
            if (k != i && k != j) {
              temp = (nodes[j].a - nodes[i].a) * (nodes[k].a - nodes[i].a) +
                     (nodes[j].b - nodes[i].b) * (nodes[k].b - nodes[i].b) +
                     (nodes[j].c - nodes[i].c) * (nodes[k].c - nodes[i].c) +
                     (nodes[j].d - nodes[i].d) * (nodes[k].d - nodes[i].d) +
                     (nodes[j].e - nodes[i].e) * (nodes[k].e - nodes[i].e);
              if (temp > 0) {
                k = n + 1;
                j = n + 1;
                flag = false;
              } else {
                vis[j] = 1;
                vis[k] = 1;
              }
            }
      if (flag) {
        cnt++;
        ans[cnt] = i;
      }
    }
  cout << cnt << endl;
  for (int i = 1; i <= cnt; i++) cout << ans[i] << endl;
  return 0;
}
