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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys

ri = lambda: int(sys.stdin.readline())
rl = lambda: list(map(int, sys.stdin.readline().split()))

a = ri()
li = sorted(rl(), reverse=True)
cnt = 0
for i in range(a-2):
    for j in range(i+1, a-1):
        left = j+1
        right = a
        lii = li[i]
        lij = li[j]
        if lii >= lij + li[j+1]:
            continue
        while right-left > 1:
            t = (left + right)//2
            lit = li[t]
            if lii < lij + lit:
                left = t
            else:
                right = t
        cnt += left-j
print(cnt)