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 sys

def bi_search(array, target):
    l, r = -1, len(array)-1
    while r-l > 1:
        mid = int((r+l)/2)
        if array[mid] > target:
            r = mid
        else:
            l = mid
    return r

N = int(sys.stdin.readline().strip())
l_list = list(sorted(list(map(int, sys.stdin.readline().strip().split(" ")))))
count = 0
#print(l_list)

for i in reversed(range(N)):
    a = l_list[i]
    for j in reversed(range(i)):
        b = l_list[j]
        index = bi_search(l_list[:j], a-b)
        """
        print("====")
        print(b-a)
        print(i, j, index)
        """
        if index > -1 and index < j and l_list[index] + b > a:
            count += (j-index)

print(count)