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)

from itertools import combinations
from bisect import bisect_left, bisect_right

N = int(input()) #2*10**3
L_list = [int(e) for e in input().split()]
index_list = [i for i in range(N)]

L_list.sort(reverse=False)
#print(L_list)

ans = 0

for comb in combinations(index_list, 2): #(2*10*3)*(2*10*3 -1)/2 ≒ 2*10*6
    a = L_list[comb[0]]
    b = L_list[comb[1]]
    
    #a < b+c ∴a-b < c
    #b < c+a ∴b-a < c
    if a-b > 0:
        low_limit = a-b
    else:
        low_limit = b-a
    index_left = bisect_right(L_list, low_limit) #log(2*10**6)≒6.3

    #c < a+b
    index_right = bisect_left(L_list, a+b) #log(2*10**6)
    
    #print(a,b,low_limit,a+b)
    #print(L_list[index_left:index_right])
    
    OK_c = index_right - index_left
    
    if index_left <= comb[0] <= index_right:
        OK_c -= 1
    if index_left <= comb[1] <= index_right:
        OK_c -= 1
        
    #print(OK_c)
    ans += OK_c
    
print(ans//3)