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)

import bisect

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

chouhen = []
kosuu = 0

for i in range(N):
    for j in range(i+1, N):
        a, b = min(L[i], L[j]), max(L[i], L[j])
        chouhen.append((a, b))

L.sort()

for hen in chouhen:
    hidari = max(hen[0] - hen[1], hen[1] - hen[0])
    migi = sum(hen)

    hidari_idx = bisect.bisect_right(L, hidari)
    migi_idx = bisect.bisect_left(L, migi)

    # print(hidari, migi, hidari_idx, migi_idx)

    if L[hidari_idx] <= hen[0] <= L[migi_idx - 1]:
        kosuu -= 1
    if L[hidari_idx] <= hen[1] <= L[migi_idx - 1]:
        kosuu -= 1

    kosuu += migi_idx - hidari_idx

print(max(0, kosuu // 3))