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.
#include <bits/stdc++.h>
using namespace std;
struct coord {
  int a, b, c, d, e;
  bool f;
};
const double pi = 3.1415926535 / 2.0;
double sc_product(coord x, coord y) {
  return x.a * y.a + x.b * y.b + x.c * y.c + x.d * y.d + x.e * y.e;
}
double angle(coord x, coord y) {
  return acos(sc_product(x, y) / sqrt(sc_product(x, x)) /
              sqrt(sc_product(y, y)));
}
bool check(int ind, vector<coord> &a) {
  for (int i = 0; i < a.size(); ++i) {
    for (int j = 0; j < a.size(); ++j) {
      if (i != ind && j != ind && i != j) {
        coord x1 = {a[i].a - a[ind].a, a[i].b - a[ind].b, a[i].c - a[ind].c,
                    a[i].d - a[ind].d, a[i].e - a[ind].e, false};
        coord x2 = {a[j].a - a[ind].a, a[j].b - a[ind].b, a[j].c - a[ind].c,
                    a[j].d - a[ind].d, a[j].e - a[ind].e, false};
        if (angle(x1, x2) < pi) {
          a[ind].f = true;
          return false;
        }
      }
    }
  }
  return true;
}
int main() {
  int n;
  cin >> n;
  vector<coord> a;
  for (int i = 0; i < n; ++i) {
    coord tmp;
    cin >> tmp.a >> tmp.b >> tmp.c >> tmp.d >> tmp.e;
    tmp.f = false;
    a.push_back(tmp);
  }
  if (n == 1) {
    cout << '1' << endl << '1';
  } else {
    if (n == 2) {
      cout << '2' << endl << '1' << endl << '2';
    } else {
      bool f = false;
      for (int i = 1; i < n; ++i) {
        for (int j = 1; j < n; ++j) {
          if (j != i) {
            coord x1 = {a[i].a - a[0].a, a[i].b - a[0].b, a[i].c - a[0].c,
                        a[i].d - a[0].d, a[i].e - a[0].e, false};
            coord x2 = {a[j].a - a[0].a, a[j].b - a[0].b, a[j].c - a[0].c,
                        a[j].d - a[0].d, a[j].e - a[0].e, false};
            if (angle(x1, x2) >= pi && !a[0].f) {
              if (check(0, a)) {
                cout << '1' << endl << '1';
                f = true;
                break;
              }
            }
            x1 = {a[0].a - a[i].a, a[0].b - a[i].b, a[0].c - a[i].c,
                  a[0].d - a[i].d, a[0].e - a[i].e, false};
            x2 = {a[j].a - a[i].a, a[j].b - a[i].b, a[j].c - a[i].c,
                  a[j].d - a[i].d, a[j].e - a[i].e, false};
            if (angle(x1, x2) >= pi && !a[i].f) {
              if (check(i, a)) {
                cout << '1' << endl << i + 1;
                f = true;
                break;
              }
            }
            x1 = {a[0].a - a[j].a, a[0].b - a[j].b, a[0].c - a[j].c,
                  a[0].d - a[j].d, a[0].e - a[j].e, false};
            x2 = {a[i].a - a[j].a, a[i].b - a[j].b, a[i].c - a[j].c,
                  a[i].d - a[j].d, a[i].e - a[j].e, false};
            if (angle(x1, x2) >= pi && !a[j].f) {
              if (check(j, a)) {
                cout << '1' << endl << j + 1;
                f = true;
                break;
              }
            }
          }
        }
        if (f) {
          break;
        }
      }
      if (!f) {
        cout << '0';
      }
    }
  }
  return 0;
}
