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 judge(a,b,c){
  if( a >= b+c ){
    return false;
  }
  if( b >= a+c ){
    return false;
  }
  if( c >= a+b ){
    return false;
  }
  return true;
}
function Main(input){
  input = input.split("\n");
  inputStr = input[0].split(" ");
  const N = Number.parseInt(inputStr[0]);
  inputStr = input[1].split(" ");
  var L = inputStr.map(inputStr => Number.parseInt(inputStr));
  //a,b,c其々を表す3重のループを組んで全探索
  //各結果毎に計算して結果をansに足し込む
  var ans = 0;
  for(var i=0 ; i<N-2 ; i++){
    for(var j=i+1 ; j<N-1 ; j++){
      for(var k=j+1 ; k<N ; k++){
        var a = L[i];
        var b = L[j];
        var c = L[k];
        //条件判断
        if( judge(a,b,c) === true){
          //console.log(a,b,c);
          ans++;
        }
      }
    }
  }
  console.log(ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));