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)

n = int(input())
ln = list(map(int, input().split()))

ln.sort()

def binary_search(x, r):
    left = r + 1
    right = n - 1
    while left <= right:
        mid = (left + right) // 2
        if ln[mid] == x:
            return mid
        elif ln[mid] > x:
            right = mid - 1
        else:
            left = mid + 1
    if ln[mid] > x:
        return mid - 1
    else:
        return mid


ans = 0
for a in range(n-2):
    for b  in range(a+1, n-1):
        cmax = ln[b] + ln[a] - 1
        ans += max(0, binary_search(cmax, b) - b)

print(ans)