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: Wrong Answer)

N=int(input())
L=sorted(list(map(int,input().split())))
L=[3,1,5,1,2,3,4,1,5,2,1,3,]
L=list(set(L))
N=len(L)
print(L)
exit()
count=0
d2breakFlag=False
for d1 in range(N-2):
    for d2 in range(d1+1,N-1):
        Temp=L[d1]+L[d2]

        """for d3 in range(d2+1,N):
            if L[d1]+L[d2]>L[d3]:count+=1
            else:break
print(count)"""