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 = sorted(list(map(int, input().split())))

counter = 0
for a_pointer in range(len(L)):
    for b_pointer in range(a_pointer+1, len(L)):
        a = L[a_pointer]
        b = L[b_pointer]
        c_left_pointer = max(bisect.bisect_left(L, b - a + 1), b_pointer + 1)
        c_right_pointer = bisect.bisect_right(L, b + a - 1)
        #print(a, b, c_left_pointer, c_right_pointer)
        counter += max(c_right_pointer - c_left_pointer, 0)
        #if c_right_pointer == len(L) and c_right_pointer == len(L):
            #break
print(counter)