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: Wrong Answer)

from itertools import combinations
from bisect import bisect_right, bisect_left

N = int(input())
L = sorted([int(i) for i in input().split()])
ans = 0

for i,j in combinations(range(N), 2):
    a, b = L[i], L[j]    
    if b - a >= a:
        continue
    x = bisect_right(L, a)
    y = bisect_left(L, b-a+1)
    ans += x - y
    if y <= i < x:
        ans -= 1
    if y <= j < x:
        ans -= 1
print(ans)