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)

import bisect
def main():
    n=int(input())
    l=sorted(list(map(int,input().split(' '))))
    ans = 0
    for n,i in enumerate(l):
        for m,j in enumerate(l[n+1:]):
                ans +=bisect.bisect_left(l,i+j) - bisect.bisect_right(l,abs(i-j))
                if abs(i-j)<i<i+j:
                    ans -=1
                if abs(i-j)<j<i+j:
                    ans -=1
    print(ans//3)
if __name__ == '__main__':
    main()