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) {
  input = input.split("\n");
  var N = input[0];
  var L = input[1].split(" ").map(Number);
  var sum = 0;
  L.sort(function(a,b){return b-a;});
  for(var i=0;i<N-1;i++){
    for(var j=i+1;j<N;j++){
      var tag = L[i]-L[j];
      var arr = L.slice(0,L.length);
      arr.splice(0,j+1);
      arr.reverse();
      sum += arr.length-caninsert(arr,tag);
    //  console.log(tag,caninsert(arr,tag),arr)
    }
  }
  console.log(sum);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));
//以下写経。C++なら関数が用意されてるし多少はね…？
function caninsert(array, value){
  value += 0.1
    var lower = 0;
    var upper = array.length;

    while ( lower < upper ) {

        var mid = Math.floor(lower + (upper - lower) / 2);

        if ( array[mid] <= value ) {
            lower = mid + 1;
        } else {
            upper = mid;
        }

    }
    return lower;

};