Given an array ~A~ consisting of ~n~ positive integers ~A_1, A_2, \ldots, A_n~, with each element has a value not exceeding ~10^9~.

• A triplet of numbers is called a triangle triplet if these three numbers can form the sides of a triangle.

Requirement: Count how many triangle triplets ~(A_i, A_j, A_k)~ there are in the array ~A~, where ~i, j, k~ are all distinct.

Input

• The first line contains the integer ~n~ ~(1 < n \leq 5 \times 10^3)~.
• The second line contains the elements of the array ~A~, separated by spaces.

Output

• Output the number of triangle triplets.

Sample Input

5
4 3 1 5 7 

Sample Output

3