Problem Statement

Takahashi has $N$ sticks that are distinguishable from each other. The length of the $i$-th stick is $L_i$.

He is going to form a triangle using three of these sticks. Let $a$, $b$, and $c$ be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

• $a < b + c$
• $b < c + a$
• $c < a + b$

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

• All values in input are integers.
• $3 \leq N \leq 2 \times 10^3$
• $1 \leq L_i \leq 10^3$

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.