Problem Description

Avin is studying isosceles trapezoids. An isosceles trapezoid is a convex quadrilateral with two opposite parallel bases, two equal-length legs and positive area. In this problem, we further require that the two legs are not parallel. Given n segments, you are asked to find the number of isosceles trapezoids whose 4 edges are from these segments and the greatest common divisor of their lengths is 1. Two congruent isosceles trapezoids are counted only once.

Input

The first line contains a number n (4 ≤ n ≤ 2, 000). The second line contains n numbers, each of which represents the length of a segment (the length is within [2, 10000]).

Output

Print the number of non-congruent isosceles trapezoids.

5
4 4 2 8 9
6
4 4 4 2 8 9

2
3