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)

import sys; readline = sys.stdin.readline
from collections import deque


N = int(readline())
L = list(map(int, readline().split()))

L.sort()

Ns = [0] * (2*10**3 + 10)

for l in L:
    Ns[l] += 1

cNs = [0] * len(Ns)
for i in range(1, len(Ns)):
    cNs[i] = cNs[i - 1] + Ns[i]

count = 0
for i in range(N - 1, -1, -1):
    for j in range(i - 1, -1, -1):
        m = L[i] - L[j]
        M = L[j] - 1
        count += max(0, cNs[M] - cNs[m])

        if L[j] == m:
            count += max(0, Ns[L[j]] - 1)
        

print(count)