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)

N = int(input())
L = [i for i in map(int, input().split())]

L = sorted(L)[::-1] # descending order

def binary_search(descend_list, threshold):
    # 閾値を超えている要素の数を返す
    length = len(descend_list)
    
    # 最小の数が閾値を超えればリストの長さを返す
    if descend_list[-1] > threshold:
        return length
    
    # 最大の数が閾値を超えなければ0を返す
    if descend_list[0] <= threshold:
        return 0
    
    # 二分探索する 少なくとも一つはthresholdを超える要素があり、少なくとも一つはthresholdを超えない要素がある場合
    upper_bound = length
    lower_bound = 0
    index = (upper_bound - lower_bound) // 2
    
    while upper_bound > lower_bound + 1:
        if descend_list[index] > threshold:
            lower_bound = index
        else:
            upper_bound = index
        
        index = (upper_bound + lower_bound) // 2
    
    return lower_bound + 1

i = 0
ret = 0

while i < N - 2:
    edge1 = L[i]
    for j in range(i + 1, N-1):
        edge2 = L[j]
        _ret = binary_search(L[j+1:], edge1 - edge2)
        if _ret == 0:
            break
        else:
            ret += _ret
    
    i += 1

print(ret)