#include <bits/stdc++.h>
using namespace std;
int INF = 0x3f3f3f3f;
const int N = 1111;
struct point {
  int a, b, c, d, e;
} P[N];
int res[N];
bool fun1(point X, point Y, point Z) {
  if ((Y.a - X.a) * (Z.a - X.a) + (Y.b - X.b) * (Z.b - X.b) +
          (Y.c - X.c) * (Z.c - X.c) + (Y.d - X.d) * (Z.d - X.d) +
          (Y.e - X.e) * (Z.e - X.e) >
      0)
    return 1;
  return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n, ans = 0;
  cin >> n;
  for (int i = 1; i <= n; i++)
    cin >> P[i].a >> P[i].b >> P[i].c >> P[i].d >> P[i].e;
  if (n > 243) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    int idx = 1;
    for (int j = 1; j <= n; j++) {
      if (j == i) continue;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        if (fun1(P[i], P[j], P[k])) {
          idx = 0;
          break;
        }
      }
      if (idx == 0) break;
    }
    if (idx == 1) {
      ans++;
      res[ans] = i;
    }
  }
  if (ans == 0) {
    cout << ans << endl;
    return 0;
  }
  cout << ans << endl;
  for (int i = 1; i <= ans; i++) cout << res[i] << endl;
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

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;
int INF = 0x3f3f3f3f;
const int N = 1111;
struct point {
  int a, b, c, d, e;
} P[N];
int res[N];
bool fun1(point X, point Y, point Z) {
  if ((Y.a - X.a) * (Z.a - X.a) + (Y.b - X.b) * (Z.b - X.b) +
          (Y.c - X.c) * (Z.c - X.c) + (Y.d - X.d) * (Z.d - X.d) +
          (Y.e - X.e) * (Z.e - X.e) >
      0)
    return 1;
  return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n, ans = 0;
  cin >> n;
  for (int i = 1; i <= n; i++)
    cin >> P[i].a >> P[i].b >> P[i].c >> P[i].d >> P[i].e;
  if (n > 243) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 1; i <= n; i++) {
    int idx = 1;
    for (int j = 1; j <= n; j++) {
      if (j == i) continue;
      for (int k = 1; k <= n; k++) {
        if (k == i || k == j) continue;
        if (fun1(P[i], P[j], P[k])) {
          idx = 0;
          break;
        }
      }
      if (idx == 0) break;
    }
    if (idx == 1) {
      ans++;
      res[ans] = i;
    }
  }
  if (ans == 0) {
    cout << ans << endl;
    return 0;
  }
  cout << ans << endl;
  for (int i = 1; i <= ans; i++) cout << res[i] << endl;
  return 0;
}

```