D - Triangles

Score : $400$ points

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.

4
3 4 2 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

3
1 1000 1

0

No triangles can be formed.

7
218 786 704 233 645 728 389

23