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: Time Limit Exceeded)

function main(input){
  var num = 0;//合計
  var i = 0;//１本目カウンタ
  var counter = 1;//２本目カウンタ
  var thcount = 2;//３本目カウンタ
  var inputN;
  var inputD;
  input = input.split('\n');
  inputN = parseInt(input[0]);
  inputD =  input[1].split(' ');

  for(i=0;i<inputN-2;i++){
    for(counter=i+1;counter<inputN-1;counter++){
      for(thcount=counter+1;thcount<inputN;thcount++){
        if(i!=counter && i != thcount && counter!=thcount){
          if(parseInt(inputD[i])<parseInt(inputD[counter]) + parseInt(inputD[thcount]) && parseInt(inputD[counter])<parseInt(inputD[thcount]) + parseInt(inputD[i]) && parseInt(inputD[thcount]) < parseInt(inputD[i]) + parseInt(inputD[counter])){
            num++;
          }
        }
      }
    }
  }
  console.log(num);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));