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>
const int MAX_LEN = 1010;
using namespace std;
template <typename U, typename V>
string to_string(pair<U, V>);
string to_string(const string& e_) { return "\"" + e_ + "\""; }
string to_string(char e_) { return "\'" + string(1, e_) + "\'"; }
string to_string(bool e_) { return e_ ? "true" : "false"; }
template <typename T>
string to_string(T e_) {
  string s_ = "[ ";
  for (const auto& x_ : e_) s_ += to_string(x_) + " ";
  return s_ + "]";
}
template <typename U, typename V>
string to_string(pair<U, V> e_) {
  return "(" + to_string(e_.first) + ", " + to_string(e_.second) + ")";
}
void dbg_str() { ; }
template <typename U, typename... V>
void dbg_str(U u, V... v) {
  ;
  dbg_str(v...);
}
int n, x;
vector<int> points[15];
double ninety = acos(0);
double calcangle(int a, int b, int c) {
  double xy = 0;
  double xv = 0;
  double yv = 0;
  for (int i = 0; i < 5; i++) {
    xv += (points[a][i] - points[c][i]) * (points[a][i] - points[c][i]);
    yv += (points[b][i] - points[c][i]) * (points[b][i] - points[c][i]);
    xy += (points[a][i] - points[c][i]) * (points[b][i] - points[c][i]);
  }
  double angrad = acos(xy / (sqrt(xv) * sqrt(yv)));
  return angrad;
}
int main() {
  scanf("%d", &n);
  if (n <= 11) {
    int cur = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < 5; j++) {
        scanf("%d", &x);
        points[cur].push_back(x);
      }
      cur++;
    }
    vector<int> sol;
    ;
    ;
    for (int i = 0; i < n; i++) {
      bool all = true;
      for (int j = 0; j < n; j++) {
        for (int k = 0; k < n; k++) {
          if (i != j && j != k && i != k) {
            if (i == 0)
              ;
            if (calcangle(j, k, i) < ninety) all = false;
          }
        }
      }
      if (all) sol.push_back(i);
    }
    printf("%d\n", sol.size());
    for (int i = 0; i < sol.size(); i++) {
      printf("%d\n", sol[i] + 1);
    }
  } else
    printf("0\n");
}
