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 Pascal (FPC 2.6.2) (judge verdict: Time Limit Exceeded)

var
  n,i,j,k,sum:longint;
  a:array[0..10010] of longint;
begin
  readln(n);
for i:=1 to n do read(a[i]);
for i:=1 to n-2 do
  for j:=i+1 to n-1 do
    if j<>i then
      for k:=j+1 to n do
        if (j<>k) and (a[i]+a[j]>a[k]) and (a[i]+a[k]>a[j]) and (a[j]+a[k]>a[i]) then inc(sum);
  write(sum);
end.