#include <bits/stdc++.h>
using namespace std;
vector<tuple<int, int, int, int, int> > points;
vector<double> length[1000];
double absolute(tuple<int, int, int, int, int> x) {
  return sqrt(get<0>(x) * get<0>(x) + get<1>(x) * get<1>(x) +
              get<2>(x) * get<2>(x) + get<3>(x) * get<3>(x) +
              get<4>(x) * get<4>(x));
}
int skalar(tuple<int, int, int, int, int> x, tuple<int, int, int, int, int> y) {
  return get<0>(x) * get<0>(y) + get<1>(x) * get<1>(y) + get<2>(x) * get<2>(y) +
         get<3>(x) * get<3>(y) + get<4>(x) * get<4>(y);
}
tuple<int, int, int, int, int> diff(tuple<int, int, int, int, int> x,
                                    tuple<int, int, int, int, int> y) {
  tuple<int, int, int, int, int> z;
  get<0>(z) = get<0>(x) - get<0>(y);
  get<1>(z) = get<1>(x) - get<1>(y);
  get<2>(z) = get<2>(x) - get<2>(y);
  get<3>(z) = get<3>(x) - get<3>(y);
  get<4>(z) = get<4>(x) - get<4>(y);
  return z;
}
double angle(tuple<int, int, int, int, int> x, tuple<int, int, int, int, int> y,
             tuple<int, int, int, int, int> z) {
  return acos(skalar(diff(x, y), diff(z, y)) /
              (absolute(diff(x, y)) * absolute(diff(z, y)))) *
         180 / 3.14159265;
}
int n, a, b, c, d, e;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a >> b >> c >> d >> e;
    tuple<int, int, int, int, int> x;
    get<0>(x) = a;
    get<1>(x) = b;
    get<2>(x) = c;
    get<3>(x) = d;
    get<4>(x) = e;
    points.push_back(x);
  }
  if (n == 1) {
    cout << 1 << endl << 1;
    return 0;
  } else if (n == 2) {
    cout << 2 << endl << 1 << endl << 2;
    return 0;
  }
  tuple<double, int, int> lo;
  get<0>(lo) = 1000000000;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      double len = absolute(diff(points[j], points[i]));
      if (len < get<0>(lo)) {
        get<0>(lo) = len;
        get<1>(lo) = i;
        get<2>(lo) = j;
      }
    }
  }
  int no = 0;
  while (no == get<1>(lo) || no == get<2>(lo)) no++;
  double ang1 = angle(points[no], points[get<1>(lo)], points[get<2>(lo)]);
  double ang2 = angle(points[no], points[get<2>(lo)], points[get<1>(lo)]);
  if (ang1 >= 90) {
    for (int i = 0; i < n; i++) {
      if (i == get<1>(lo)) continue;
      for (int j = i + 1; j < n; j++) {
        if (i == get<1>(lo)) continue;
        double angtemp = angle(points[j], points[get<1>(lo)], points[i]);
        if (angtemp < 90) {
          cout << 0;
          return 0;
        } else if (angtemp == 0 || angtemp == 180) {
          if (absolute(diff(points[j], points[get<1>(lo)])) +
                  absolute(diff(points[get<1>(lo)], points[i])) ==
              absolute(diff(points[j], points[i]))) {
            continue;
          } else {
            cout << 0;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl << get<1>(lo) + 1;
    return 0;
  } else if (ang2 >= 90) {
    for (int i = 0; i < n; i++) {
      if (i == get<2>(lo)) continue;
      for (int j = i + 1; j < n; j++) {
        if (i == get<2>(lo)) continue;
        double angtemp = angle(points[j], points[get<2>(lo)], points[i]);
        if (angtemp < 90) {
          cout << 0;
          return 0;
        } else if (angtemp == 0 || angtemp == 180) {
          if (absolute(diff(points[j], points[get<2>(lo)])) +
                  absolute(diff(points[get<2>(lo)], points[i])) ==
              absolute(diff(points[j], points[i]))) {
            continue;
          } else {
            cout << 0;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl << get<2>(lo) + 1;
    return 0;
  } else {
    cout << 0;
    return 0;
  }
}

### Prompt

Develop a solution in cpp 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;
vector<tuple<int, int, int, int, int> > points;
vector<double> length[1000];
double absolute(tuple<int, int, int, int, int> x) {
  return sqrt(get<0>(x) * get<0>(x) + get<1>(x) * get<1>(x) +
              get<2>(x) * get<2>(x) + get<3>(x) * get<3>(x) +
              get<4>(x) * get<4>(x));
}
int skalar(tuple<int, int, int, int, int> x, tuple<int, int, int, int, int> y) {
  return get<0>(x) * get<0>(y) + get<1>(x) * get<1>(y) + get<2>(x) * get<2>(y) +
         get<3>(x) * get<3>(y) + get<4>(x) * get<4>(y);
}
tuple<int, int, int, int, int> diff(tuple<int, int, int, int, int> x,
                                    tuple<int, int, int, int, int> y) {
  tuple<int, int, int, int, int> z;
  get<0>(z) = get<0>(x) - get<0>(y);
  get<1>(z) = get<1>(x) - get<1>(y);
  get<2>(z) = get<2>(x) - get<2>(y);
  get<3>(z) = get<3>(x) - get<3>(y);
  get<4>(z) = get<4>(x) - get<4>(y);
  return z;
}
double angle(tuple<int, int, int, int, int> x, tuple<int, int, int, int, int> y,
             tuple<int, int, int, int, int> z) {
  return acos(skalar(diff(x, y), diff(z, y)) /
              (absolute(diff(x, y)) * absolute(diff(z, y)))) *
         180 / 3.14159265;
}
int n, a, b, c, d, e;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a >> b >> c >> d >> e;
    tuple<int, int, int, int, int> x;
    get<0>(x) = a;
    get<1>(x) = b;
    get<2>(x) = c;
    get<3>(x) = d;
    get<4>(x) = e;
    points.push_back(x);
  }
  if (n == 1) {
    cout << 1 << endl << 1;
    return 0;
  } else if (n == 2) {
    cout << 2 << endl << 1 << endl << 2;
    return 0;
  }
  tuple<double, int, int> lo;
  get<0>(lo) = 1000000000;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      double len = absolute(diff(points[j], points[i]));
      if (len < get<0>(lo)) {
        get<0>(lo) = len;
        get<1>(lo) = i;
        get<2>(lo) = j;
      }
    }
  }
  int no = 0;
  while (no == get<1>(lo) || no == get<2>(lo)) no++;
  double ang1 = angle(points[no], points[get<1>(lo)], points[get<2>(lo)]);
  double ang2 = angle(points[no], points[get<2>(lo)], points[get<1>(lo)]);
  if (ang1 >= 90) {
    for (int i = 0; i < n; i++) {
      if (i == get<1>(lo)) continue;
      for (int j = i + 1; j < n; j++) {
        if (i == get<1>(lo)) continue;
        double angtemp = angle(points[j], points[get<1>(lo)], points[i]);
        if (angtemp < 90) {
          cout << 0;
          return 0;
        } else if (angtemp == 0 || angtemp == 180) {
          if (absolute(diff(points[j], points[get<1>(lo)])) +
                  absolute(diff(points[get<1>(lo)], points[i])) ==
              absolute(diff(points[j], points[i]))) {
            continue;
          } else {
            cout << 0;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl << get<1>(lo) + 1;
    return 0;
  } else if (ang2 >= 90) {
    for (int i = 0; i < n; i++) {
      if (i == get<2>(lo)) continue;
      for (int j = i + 1; j < n; j++) {
        if (i == get<2>(lo)) continue;
        double angtemp = angle(points[j], points[get<2>(lo)], points[i]);
        if (angtemp < 90) {
          cout << 0;
          return 0;
        } else if (angtemp == 0 || angtemp == 180) {
          if (absolute(diff(points[j], points[get<2>(lo)])) +
                  absolute(diff(points[get<2>(lo)], points[i])) ==
              absolute(diff(points[j], points[i]))) {
            continue;
          } else {
            cout << 0;
            return 0;
          }
        }
      }
    }
    cout << 1 << endl << get<2>(lo) + 1;
    return 0;
  } else {
    cout << 0;
    return 0;
  }
}

```