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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

n = int(input())
A = list(map(int, input().split()))
A = sorted(A)
ans = 0


def q(k):
    if A[k] < A[i] + A[j]:
        return True
    else:
        return False


for i in range(n):
    for j in range(i + 1, n):
        l = j
        r = n
        while r - l > 1:
            mid = (l + r) // 2
            if q(mid):
                l = mid
            else:
                r = mid
        ans += (l - j)


print(ans)