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)

# a < b + c
# b < a + C
# c < a + b

# 4 3 2 1
# a b c 

# abs(a - b) < c < a + b
# a < b < c
# b - a < b < c
# c < a + b 

from math import ceil, floor
from bisect import bisect_left, bisect_right

def solution(N, data): # O(N^2 * logN)
    data = sorted(data)
    c = 0
    for i in range(N-2):
        for j in range(i+1, N-1):
            c += bisect_left(data[j+1:], data[i] + data[j])

    return c

if __name__ == '__main__':
    N = int(input())
    L_i = list(map(int, input().split()))
    a = solution(N, L_i)
    print(a)