Problem:
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

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let ans, k, n = ref 0, ref 0, Scanf.scanf " %d" (+) 0
let ss, ls = Array.(make (n * (n - 1) / 2) 0, init n @@ fun _ -> Scanf.scanf " %d" (+) 0)
let g i k a = a.(i) > k
let f k a = let l, r = ref @@ -1, ref @@ Array.length a in while !r - !l > 1 do let m = !l + (!r - !l) / 2 in if g m k a then r := m else l := m done; !r
let _ = for i = 0 to n - 1 do for j = i + 1 to n - 1 do ss.(!k) <- ls.(i) + ls.(j); incr k done done;
  Array.(sort (-) ss; sort (fun x y -> y - x) ls; iteri (fun i l -> ans := !ans + max 0 ((n - i - 1) * (n - i - 2) / 2 - f l ss)) ls); Printf.printf "%d\n" !ans