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 args = input.split('\n').map(arg => arg.split(' '))
	const N = parseInt(args[0][0], 10)
	const L = args[1].map(arg => parseInt(arg, 10)).sort((a, b) => a - b)
	let ans = 0

	for (let i = 2; i < N; i++) {
		for (let j = 0; j < (i - 1); j++) {
			for (let k = j + 1; k < i; k++) {
				if ((L[j] + L[k]) > L[i]) ans++
			}
		}
	}
	console.log(ans)
}

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