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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input){
  inputs=input.split("\n");
  bos=inputs[1].split(" ").map(x=>parseInt(x)).sort((a,b)=>a-b);

  var num=0,a,b,c,l=inputs[0];
  for(a=0;a<l;++a){
    for(b=a+1;b<l;++b){
      for(c=l-1;c>b;--c){
        if(bos[c]<bos[a]+bos[b]){
          num+=c-b;break;
        }
      }
    }
  }

  console.log(num);
}
Main(require('fs').readFileSync('/dev/stdin','utf8'));