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)

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

counts = {}
x = v[0]
c = 0
for i in v:
    if i != x:
        counts[x] = c
        x = i
        c = 0
    c += 1
counts[x] = c

v1 = list(counts)

sums = [0]
for i in range(1, 1005):
    try:
        sums.append(v1.index(i))
    except ValueError:
        sums.append(sums[-1])


total = 0
for i, x in enumerate(v1[:n-2]):
    if x == 1:
        continue
    for j, y in enumerate(v1[i+1:n-1]):
        total += (sums[min(1004, x+y-1)] - sums[y])


for i, c in counts.items():
    if c >= 2:
        total += (sums[min(1004, 2*i-1)])




# v3
total += sum(True if c >= 3 else False for c in counts.values())


print(total)