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)

import numpy as np
import collections as cl
n=int(input())
l=np.asarray(list(map(int,input().split())))
i=np.tile(np.arange(len(l)),(n**2,1)).T.ravel()
j=np.tile(np.tile(np.arange(len(l)),(n,1)).ravel(),(n,1)).T.ravel()
k=np.tile(np.arange(n),(n**2,1)).ravel()
tmp=(l[i]<l[j]+l[k])*(l[j]<l[i]+l[k])*(l[k]<l[i]+l[j])*(i!=j)*(i!=k)*(j!=k)
tmp=np.asarray(np.where(tmp.reshape(n,n,n))).T.astype(str)
tmp.sort(axis=-1)
ans=[]
for t in tmp:
    ans.append(t[0]+t[1]+t[2])
print(len(cl.Counter(ans)))