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Contest: Task: Related: TaskC TaskE

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.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

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

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23