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 double pi = 4 * atan(1);
const int Nmax = 1001;
int d[5][Nmax];
int n;
double ang(int a, int b, int c) {
  double cp = 0, fp = 0, sp = 0;
  for (int k = 0; k < 5; k++) {
    cp += (d[k][a] - d[k][b]) * (d[k][c] - d[k][b]);
    fp += (d[k][a] - d[k][b]) * (d[k][a] - d[k][b]);
    sp += (d[k][c] - d[k][b]) * (d[k][c] - d[k][b]);
  }
  double poz = sqrt(fp) * sqrt(sp);
  return acos(cp / poz);
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    for (int k = 0; k < 5; k++) {
      cin >> d[k][i];
    }
  }
  if (n < 3) {
    cout << n << "\n1";
    if (n > 1) cout << " 2";
    cout << '\n';
    return 0;
  }
  int fr[3], ch = -1;
  fr[0] = 1;
  fr[1] = 2;
  fr[2] = 3;
  if (pi / 2.0 - ang(fr[1], fr[0], fr[2]) <= 1e-5) ch = fr[0];
  if (pi / 2.0 - ang(fr[0], fr[1], fr[2]) <= 1e-5) ch = fr[1];
  if (pi / 2.0 - ang(fr[0], fr[2], fr[1]) <= 1e-5) ch = fr[2];
  for (int i = 4; i <= n; i++) {
    if (fr[0] != ch)
      fr[0] = i;
    else if (fr[1] != ch)
      fr[1] = i;
    else if (fr[2] != ch)
      fr[2] = i;
    ch = -1;
    if (pi / 2.0 - ang(fr[1], fr[0], fr[2]) <= 1e-5) ch = fr[0];
    if (pi / 2.0 - ang(fr[0], fr[1], fr[2]) <= 1e-5) ch = fr[1];
    if (pi / 2.0 - ang(fr[0], fr[2], fr[1]) <= 1e-5) ch = fr[2];
  }
  if (ch == -1) {
    cout << 0 << '\n';
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (i != ch && j != ch) {
        if (pi / 2.0 - ang(i, ch, j) > 1e-5) {
          cout << 0 << '\n';
          return 0;
        }
      }
    }
  }
  cout << 1 << '\n';
  cout << ch << '\n';
  return 0;
}
