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.
def sc(i,j,k):
   xx=0
   for t in range(5):
      xx+=(m[i][t]-m[j][t])*(m[i][t]-m[k][t])
   return xx
n= int(input())

m=[]
mm=n
ans=[]
if (n > 36):
   print("0")
else:
   for i in range(n):
      ans.append(1)
      a,b,c,d,e=map(int,input().split())
      m.append([a,b,c,d,e])
   for i in range(n):
      for j in range(n):
         if (i != j):
            for k in range(n):
               if (i != k) and ( j != k):
                  if sc(i,j,k) >0:
                     ans[i]=-1
   for i in range(n):
      if ans[i]==-1:
         mm+=-1
   print(mm)
   for i in range(n):
      if ans[i]==1:
         print(i+1)