#include <bits/stdc++.h>
using namespace std;
int n, flag;
struct Point {
  int a, b, c, d, e;
  Point(int a = 0, int b = 0, int c = 0, int d = 0, int e = 0)
      : a(a), b(b), c(c), d(d), e(e){};
  Point operator-(const Point& rhs) {
    return Point(a - rhs.a, b - rhs.b, c - rhs.c, d - rhs.d, e - rhs.e);
  }
} p[1005], ab, ac, bc;
int dot(Point aa, Point bb) {
  return aa.a * bb.a + aa.b * bb.b + aa.c * bb.c + aa.d * bb.d + aa.e * bb.e;
}
double xx, yy, ang;
vector<int> ans;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d%d%d%d%d", &p[i].a, &p[i].b, &p[i].c, &p[i].d, &p[i].e);
  }
  if (n > 11) {
    printf("0\n");
  } else {
    for (int i = 1; i <= n; i++) {
      flag = 0;
      for (int j = 1; j <= n; j++) {
        if (j == i) continue;
        for (int k = j + 1; k <= n; k++) {
          ab = p[j] - p[i];
          ac = p[k] - p[i];
          bc = p[k] - p[j];
          if (dot(ab, ab) + dot(ac, ac) > dot(bc, bc)) {
            flag = 1;
            break;
          }
        }
        if (flag) break;
      }
      if (!flag) {
        ans.push_back(i);
      }
    }
    printf("%d\n", ans.size());
    for (int i = 0; i < ans.size(); i++) {
      printf("%d\n", ans[i]);
    }
  }
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to 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 n, flag;
struct Point {
  int a, b, c, d, e;
  Point(int a = 0, int b = 0, int c = 0, int d = 0, int e = 0)
      : a(a), b(b), c(c), d(d), e(e){};
  Point operator-(const Point& rhs) {
    return Point(a - rhs.a, b - rhs.b, c - rhs.c, d - rhs.d, e - rhs.e);
  }
} p[1005], ab, ac, bc;
int dot(Point aa, Point bb) {
  return aa.a * bb.a + aa.b * bb.b + aa.c * bb.c + aa.d * bb.d + aa.e * bb.e;
}
double xx, yy, ang;
vector<int> ans;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d%d%d%d%d", &p[i].a, &p[i].b, &p[i].c, &p[i].d, &p[i].e);
  }
  if (n > 11) {
    printf("0\n");
  } else {
    for (int i = 1; i <= n; i++) {
      flag = 0;
      for (int j = 1; j <= n; j++) {
        if (j == i) continue;
        for (int k = j + 1; k <= n; k++) {
          ab = p[j] - p[i];
          ac = p[k] - p[i];
          bc = p[k] - p[j];
          if (dot(ab, ab) + dot(ac, ac) > dot(bc, bc)) {
            flag = 1;
            break;
          }
        }
        if (flag) break;
      }
      if (!flag) {
        ans.push_back(i);
      }
    }
    printf("%d\n", ans.size());
    for (int i = 0; i < ans.size(); i++) {
      printf("%d\n", ans[i]);
    }
  }
  return 0;
}

```