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: Wrong Answer)

let split_string ?(pattern=" ") = Str.split @@ Str.regexp pattern
let n = Scanf.sscanf (read_line ()) "%d" @@ fun n -> n
let ls = read_line () |> split_string |> List.map int_of_string |> List.sort compare |> List.rev |> Array.of_list

let rec loop ai bi l r =
  if r <= l then begin
    let l = ref l in
    while !l < n - 1 && ls.(!l + 1) = ls.(!l) do l := !l + 1 done;
    max 0 @@ !l - bi - 1
  end
  else
    let mid = (l + r) / 2 in
    let a, b, c = ls.(ai), ls.(bi), ls.(mid) in
    if a < b + c && b < c + a && c < a + b then loop ai bi (mid + 1) r
    else loop ai bi l mid

let () =
  let ans = ref 0 in
  for i = 0 to n - 3 do
    for j = i + 1 to n - 2 do
      ans := !ans + loop i j (j + 1) n
    done
  done;
  Printf.printf "%d\n" !ans