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)

def d_triangles():
    from itertools import combinations
    from bisect import bisect_right
    N = int(input())
    L = sorted([int(i) for i in input().split()])

    ans = 0
    for max_index in range(2, N):
        c = L[max_index]
        for second_index in range(max_index):
            b = L[second_index]
            other_index = bisect_right(L, c - b)
            if max_index > other_index:
                ans += max_index - other_index
                if other_index <= second_index:
                    ans -= 1
    return ans // 2

print(d_triangles())