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 = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0]);
    const L = arg[1].split(" ").map(n=>parseInt(n)).sort((a,b)=>b-a);
    
    // console.log(L);
    
    let answer = 0;
    
    // a<b<c かつ c < a+b の個数
    // cを決め打つ
    for(let i=0; i<N-2; i++) {
        const c = L[i];
        
        for(let j=i + parseInt(1); j<N-1; j++) {
            const a = L[j];
            
            for(let k=j + parseInt(1); k<N; k++) {
                const b = L[k];
                
                if(a + b > c) {
                    answer++;
                } else {
                    break;
                }
            }
        }

    }
    
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));