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: Time Limit Exceeded)

N = int(input())

L = list(map(int,input().split()))
L.sort()

import bisect
ans = 0
for i in range(N-1):
    a = L[i]
    for j in range(i+1, N):
        b = L[j]
        if j!=N-1:
            new_L = L[:i]+L[i+1:j]+L[j+1:]
        else:
            new_L = L[:i]+L[i+1:j]
        t1 = bisect.bisect_right(new_L,a+b-1)
        t2 = bisect.bisect_right(new_L,a-b)
        t3 = bisect.bisect_right(new_L,b-a)
        
        t4 = max(t2,t3)

        if t1!=t4:
            ans += t1-t4
        
ans = ans // 3
print(ans)