#include <bits/stdc++.h>
using namespace std;
long double pi = 3.1415926535897;
struct point {
  int a, b, c, d, e;
};
struct vec {
  double x1, x2, x3, x4, x5;
};
point arr[1001] = {};
double sq(double a) { return a * a; }
double dist(point first, point second) {
  double distsquare = sq(first.a - second.a) + sq(first.b - second.b) +
                      sq(first.c - second.c) + sq(first.d - second.d) +
                      sq(first.e - second.e);
  return sqrt(distsquare);
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    point blah;
    cin >> blah.a;
    cin >> blah.b;
    cin >> blah.c;
    cin >> blah.d;
    cin >> blah.e;
    arr[i] = blah;
  }
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    bool bad = false;
    for (int h = 0; h < n; h++) {
      for (int z = 0; z < n; z++) {
        if (i != h && h != z && i != z) {
          vec first;
          first.x1 = arr[h].a - arr[i].a;
          first.x2 = arr[h].b - arr[i].b;
          first.x3 = arr[h].c - arr[i].c;
          first.x4 = arr[h].d - arr[i].d;
          first.x5 = arr[h].e - arr[i].e;
          vec second;
          second.x1 = arr[z].a - arr[i].a;
          second.x2 = arr[z].b - arr[i].b;
          second.x3 = arr[z].c - arr[i].c;
          second.x4 = arr[z].d - arr[i].d;
          second.x5 = arr[z].e - arr[i].e;
          double top = first.x1 * second.x1 + first.x2 * second.x2 +
                       first.x3 * second.x3 + first.x4 * second.x4 +
                       first.x5 * second.x5;
          double firstdist = dist(arr[i], arr[h]);
          double seconddist = dist(arr[i], arr[z]);
          double angle = acos(top / (firstdist * seconddist));
          if ((angle * 180) / pi < 90) {
            bad = true;
            break;
          }
        }
      }
      if (bad == true) {
        break;
      }
    }
    if (bad == false) {
      ans.push_back(i + 1);
    }
  }
  cout << ans.size() << "\n";
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << "\n";
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long double pi = 3.1415926535897;
struct point {
  int a, b, c, d, e;
};
struct vec {
  double x1, x2, x3, x4, x5;
};
point arr[1001] = {};
double sq(double a) { return a * a; }
double dist(point first, point second) {
  double distsquare = sq(first.a - second.a) + sq(first.b - second.b) +
                      sq(first.c - second.c) + sq(first.d - second.d) +
                      sq(first.e - second.e);
  return sqrt(distsquare);
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    point blah;
    cin >> blah.a;
    cin >> blah.b;
    cin >> blah.c;
    cin >> blah.d;
    cin >> blah.e;
    arr[i] = blah;
  }
  vector<int> ans;
  for (int i = 0; i < n; i++) {
    bool bad = false;
    for (int h = 0; h < n; h++) {
      for (int z = 0; z < n; z++) {
        if (i != h && h != z && i != z) {
          vec first;
          first.x1 = arr[h].a - arr[i].a;
          first.x2 = arr[h].b - arr[i].b;
          first.x3 = arr[h].c - arr[i].c;
          first.x4 = arr[h].d - arr[i].d;
          first.x5 = arr[h].e - arr[i].e;
          vec second;
          second.x1 = arr[z].a - arr[i].a;
          second.x2 = arr[z].b - arr[i].b;
          second.x3 = arr[z].c - arr[i].c;
          second.x4 = arr[z].d - arr[i].d;
          second.x5 = arr[z].e - arr[i].e;
          double top = first.x1 * second.x1 + first.x2 * second.x2 +
                       first.x3 * second.x3 + first.x4 * second.x4 +
                       first.x5 * second.x5;
          double firstdist = dist(arr[i], arr[h]);
          double seconddist = dist(arr[i], arr[z]);
          double angle = acos(top / (firstdist * seconddist));
          if ((angle * 180) / pi < 90) {
            bad = true;
            break;
          }
        }
      }
      if (bad == true) {
        break;
      }
    }
    if (bad == false) {
      ans.push_back(i + 1);
    }
  }
  cout << ans.size() << "\n";
  for (int i = 0; i < ans.size(); i++) {
    cout << ans[i] << "\n";
  }
}

```