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())
L = list(map(int, input().split()))
L.sort()
ans = 0
for i in range(1, N - 1):
    for j in range(i + 1, N):
        l = L[j] - L[i]
        a = 0
        b = i - 1
        while b - a > 1:
            if L[(a + b) // 2] > l:
                b = (a + b) // 2
            else:
                a = (a + b) // 2
        if L[a] > l:
            ans += i
        elif L[b] > l:
            ans += i - b
print(ans)