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 (7.3.0) (judge verdict: Accepted)

n=int(input())
l=[int(x) for x in input().split()]

l.sort()
ans=0

for i in range(len(l)-2):
    for j in range(i+2,len(l)):
        a=l[i]
        c=l[j]
        b_min=i+1
        b_max=j-1
        while b_max-b_min>1:
            if l[(b_max+b_min)//2]>c-a:
                b_max=(b_max+b_min)//2
            else:
                b_min=(b_max+b_min)//2
        if l[b_min]>c-a:ans+=j-b_min
        elif l[b_max]>c-a:ans+=j-b_max
print(ans)