#include <bits/stdc++.h>
using namespace std;
long long MOD = 1e9 + 7;
bool debug = 0;
class pt {
 public:
  long long a, b, c, d, e;
  pt() {}
  pt(long long a, long long b, long long c, long long d, long long e)
      : a(a), b(b), c(c), d(d), e(e) {}
  long long operator*(pt p2) {
    return a * p2.a + b * p2.b + c * p2.c + d * p2.d + e * p2.e;
  }
  pt operator-(pt p2) {
    return pt(a - p2.a, b - p2.b, c - p2.c, d - p2.d, e - p2.e);
  }
  long double mod() {
    return sqrt((long double)a * a + b * b + c * c + d * d + e * e);
  }
};
vector<pt> v;
int main() {
  int n;
  cin >> n;
  v.resize(n);
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld%lld%lld%lld", &v[i].a, &v[i].b, &v[i].c, &v[i].d, &v[i].e);
  }
  vector<bool> pos(n, 1);
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      int ib = i + 1, ic = i + 2;
      while (ic < n) {
        pt v1 = v[ib] - v[i];
        pt v2 = v[ic] - v[i];
        if (acos((long double)(v1 * v2) / (v1.mod() * v2.mod())) >=
            acos(-1.0L) / 2.l) {
          pos[ib] = 0;
          pos[ic] = 0;
        } else {
          pos[i] = 0;
          goto next;
        }
        ic += 2;
        ib += 2;
      }
    }
  next:
    continue;
  }
  long long tot = 0;
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      if (debug) cout << "------" << endl;
      ;
      if (debug) cout << "------" << endl;
      ;
      if (debug)
        cout << "i"
             << " = " << (i) << endl;
      tot++;
      for (int j = 0; j < n; j++) {
        for (int k = 0; k < n; k++) {
          if (i != j and i != k and j != k) {
            pt v1 = v[j] - v[i];
            pt v2 = v[k] - v[i];
            if (acos((long double)(v1 * v2) / (v1.mod() * v2.mod())) <
                acos(-1.0L) / 2.l) {
              pos[i] = 0;
              tot--;
              goto next2;
            }
          }
        }
      }
    }
  next2:
    continue;
  }
  cout << tot << endl;
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      printf("%d ", i + 1);
    }
  }
  printf("\n");
  return 0;
}

### Prompt

Please formulate 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;
long long MOD = 1e9 + 7;
bool debug = 0;
class pt {
 public:
  long long a, b, c, d, e;
  pt() {}
  pt(long long a, long long b, long long c, long long d, long long e)
      : a(a), b(b), c(c), d(d), e(e) {}
  long long operator*(pt p2) {
    return a * p2.a + b * p2.b + c * p2.c + d * p2.d + e * p2.e;
  }
  pt operator-(pt p2) {
    return pt(a - p2.a, b - p2.b, c - p2.c, d - p2.d, e - p2.e);
  }
  long double mod() {
    return sqrt((long double)a * a + b * b + c * c + d * d + e * e);
  }
};
vector<pt> v;
int main() {
  int n;
  cin >> n;
  v.resize(n);
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld%lld%lld%lld", &v[i].a, &v[i].b, &v[i].c, &v[i].d, &v[i].e);
  }
  vector<bool> pos(n, 1);
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      int ib = i + 1, ic = i + 2;
      while (ic < n) {
        pt v1 = v[ib] - v[i];
        pt v2 = v[ic] - v[i];
        if (acos((long double)(v1 * v2) / (v1.mod() * v2.mod())) >=
            acos(-1.0L) / 2.l) {
          pos[ib] = 0;
          pos[ic] = 0;
        } else {
          pos[i] = 0;
          goto next;
        }
        ic += 2;
        ib += 2;
      }
    }
  next:
    continue;
  }
  long long tot = 0;
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      if (debug) cout << "------" << endl;
      ;
      if (debug) cout << "------" << endl;
      ;
      if (debug)
        cout << "i"
             << " = " << (i) << endl;
      tot++;
      for (int j = 0; j < n; j++) {
        for (int k = 0; k < n; k++) {
          if (i != j and i != k and j != k) {
            pt v1 = v[j] - v[i];
            pt v2 = v[k] - v[i];
            if (acos((long double)(v1 * v2) / (v1.mod() * v2.mod())) <
                acos(-1.0L) / 2.l) {
              pos[i] = 0;
              tot--;
              goto next2;
            }
          }
        }
      }
    }
  next2:
    continue;
  }
  cout << tot << endl;
  for (int i = 0; i < n; i++) {
    if (pos[i]) {
      printf("%d ", i + 1);
    }
  }
  printf("\n");
  return 0;
}

```