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 PyPy2 (5.6.0) (judge verdict: Accepted)

from bisect import bisect_right as binser
n = int(input())
l = [int(j) for j in raw_input().split()]
l = sorted(l)
ans = 0 
for i in range(1,n):
    for j in range(i):
        a = l[i] - l[j]
        x = binser(l,a, j+1, i)
        # if i-x:
        #     print(x, j+1, i-1)
        if l[x] == a:
            x = x+1
        ans+=(i-x)
        # print(i-x, a, l[x], l[j], l[i])
        # print(l[x], l[i],l[j])
print(ans)