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 N = 1005;
int sop[N][5];
int n;
bool isresult = false;
int res = 0;
bool isgood(int a, int b, int c) {
  int ans = 0;
  for (int i = 0; i < 5; i++) {
    ans += ((sop[a][i] - sop[b][i]) * (sop[a][i] - sop[c][i]));
  }
  return ans <= 0;
}
int main() {
  cin >> n;
  if (n <= 2) {
    cout << n << endl;
    for (int i = 1; i <= n; i++) cout << i << endl;
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d %d %d %d %d", sop[i], sop[i] + 1, sop[i] + 2, sop[i] + 3,
          sop[i] + 4);
  }
  int gupb = n / 3;
  for (int i = n + 1; i <= gupb * 3 + 3; i++) {
    memcpy(sop[i], sop[i - n], 5 * sizeof(int));
  }
  for (int i = 0; i <= gupb; i++) {
    if (isgood(i * 3 + 1, i * 3 + 2, i * 3 + 3)) {
      int a = i * 3 + 1;
      bool okbit = true;
      for (int j = 1; j <= n; j++) {
        if (j == a) continue;
        for (int k = j + 1; k <= n; k++) {
          if (k == a) continue;
          if (!isgood(a, k, j)) {
            okbit = false;
            break;
          }
        }
        if (!okbit) break;
      }
      if (okbit) {
        isresult = true;
        res = i * 3 + 1;
        break;
      }
    }
    if (isgood(i * 3 + 2, i * 3 + 1, i * 3 + 3)) {
      int a = i * 3 + 2;
      bool okbit = true;
      for (int j = 1; j <= n; j++) {
        if (j == a) continue;
        for (int k = j + 1; k <= n; k++) {
          if (k == a) continue;
          if (!isgood(a, k, j)) {
            okbit = false;
            break;
          }
        }
        if (!okbit) break;
      }
      if (okbit) {
        isresult = true;
        res = i * 3 + 2;
        break;
      }
    }
    if (isgood(i * 3 + 3, i * 3 + 2, i * 3 + 1)) {
      int a = i * 3 + 3;
      bool okbit = true;
      for (int j = 1; j <= n; j++) {
        if (j == a) continue;
        for (int k = j + 1; k <= n; k++) {
          if (k == a) continue;
          if (!isgood(a, k, j)) {
            okbit = false;
            break;
          }
        }
        if (!okbit) break;
      }
      if (okbit) {
        isresult = true;
        res = i * 3 + 3;
        break;
      }
    }
  }
  if (isresult) {
    cout << 1 << "\n" << res << endl;
  } else
    cout << 0 << endl;
  return 0;
}
