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 (3.4.3) (judge verdict: Runtime Error)

N = int(input().split())
ns = input().split()

dic = {}

for i in range(N):
  	if(ns[i] in dic.keys() and dic[ns[i]]<2):
    	dic[ns[i]] += 1
    elif(ns[i] not in dic.keys()):
      	dic[ns[i]] = 1

a,b,c = 0,0,0
for i in range(N):
  	if(dic[ns[i]] == 1):
      	a += 1
    elif(dic[ns[i]] == 2):
      	b += 1
    elif(dic[ns[i]] == 3):
      	c += 1

unique = a+b+c
sum_ = 0

sum_ += c
sum_ += (b+c)*(unique-1)
sum_ += unique*(unique-1)*(unique-2)/6

print(sum_)