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)

'use strict';
const main = input => {
  const n = parseInt(input[0]);
  const l = input[1].split(' ').map(val => parseInt(val));
  // console.log(n, l);
  let count = 0;
  for(let i=0; i<n-2; i++) {
    for(let j=i+1; j<n-1; j++) {
      for(let k=j+1; k<n; k++) {
        if (l[i] < l[j] + l[k] && l[j] < l[i] + l[k] && l[k] < l[i] + l[j]) {
          count++;
        }
      }
    }
  }
  console.log(count);
  
}
main(require("fs").readFileSync("/dev/stdin", "utf8").split('\n'));