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: Accepted)

from itertools import *
N = int(input())
csum = list(0 for _ in range(2000+1))
L = []
for l in map(int,input().split()):
    L.append(l)
    csum[l] += 1
csum = list(accumulate(csum))
ans = 0
for ib in range(N):
    for ia in range(ib):
        a, b = L[ia], L[ib]
        minL, maxL = abs(a-b), a+b
        ans += csum[maxL-1] - csum[minL]
        if minL < a and a < maxL: ans -= 1
        if minL < b and b < maxL: ans -= 1
print(ans//3)