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 and is acute (i.e. strictly less than ). Otherwise, the point is called good . The angle between vectors and in 5-dimensional space is defined as , where is the scalar product and is length of . Given the list of points, print the indices of the good points in ascending order. The first line of input contains a single integer n ( 1 ≤ n ≤ 10 3 ) — the number of points. The next n lines of input contain five integers a i , b i , c i , d i , e i ( | a i |, | b i |, | c i |, | d i |, | e i | ≤ 10 3 ) — the coordinates of the i-th point. All points are distinct. 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. In the first sample, the first point forms exactly a 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: We can see that all angles here are acute, so no points are good.