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: Time Limit Exceeded)

N = int(input())
L = list(map(int,input().split()))
A = [0]*1000
B = [0]*1000
ans = 0
for i in range(N):
    A[L[i]-1] += 1
B[0] = A[0]
for i in range(1,1000):
    B[i] = B[i-1]+A[i]
for i in range(N):
    for j in range(i+1,N):
        m = min([1000,L[i]+L[j]])
        n = max([L[i]-L[j],L[j]-L[i]])
        if n < L[i] and n < L[j]:
            r = 2
        elif n < L[i] or n < L[j]:
            r = 1
        else:
            r = 0
        ans += max([B[m-2] - B[n-1]-r,0])
print(ans//3)