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: Runtime Error)

// inputに入力データ全体が入る
function Main(input) {
  // 1行目がinput[0], 2行目がinput[1], …に入る
  input = input.split("\n");
  let num = parseInt(input[0], 10);
  let array = input[1].split(' ');
  
  let count = 0;
  
  for(var s=0; s<num-2; s++) {
    let a = parseInt(array[s], 10);
    
    for(var r=s+1; r<num-1; r++) {
      let b = parseInt(array[r], 10);
      
      for(var q=r+1; q<num; q++) {
        let c = parseInt(array[q], 10);
        
        if(Math.abs(b-c) < a){
            if(a < b+c){
                          count++;

            }
        }
      }
    }
  }
  
  //出力
  console.log(count);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));