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: Accepted)

from collections import Counter
n = int(input())
l = list(map(int, input().split()))
memo = [[0] for i in range(n)]
for j in range(n):
    c = Counter(l[j:])
    tmp = 0
    for i in range(1000):
        if c[i+1]:
            tmp  += c[i+1]
        memo[j].append(tmp)

ans = 0
for i in range(n):
    for j in range(i+1, n - 1):
        b = l[i]
        c = l[j]
        lo = abs(b - c)
        up = min(b + c, 1001)
        ans += memo[j+1][up-1] - memo[j+1][lo]
print(ans)