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(reverse=True)
ans = 0
for i in range(n-2):
    for j in range(i+1,n-1):
        a = l[i]
        b = l[j]
        x = (a+1) - b
        y = (b+1) - a
        z = max(x,y)
        a = j+1
        b = n-1
        c = (a+b) // 2
        while a <= b:
            if l[c] == z:
                a += 1
            elif l[c] > z:
                a = c + 1
            elif l[c] < z:
                b = c - 1
            else:
                pass
            c = (a+b) // 2
        ans += c-j
print(ans)