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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())
v = list(sorted(map(int, input().split())))
v.append(2000)
total = n*(n-1)*(n-2) / 6



def bs(left, s):
    right = n+1
    while left < right-1:
        m = (right+left)//2

        if v[m]>=s:
            right = m
        else:
            left = m
    return left+1






for i, x in enumerate(v[:-2]):
    for j, y in enumerate(v[i+1:-1]):
        k = bs(j+1, y+x)
        total -= (n-k)

print(int(total))