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)

import bisect

# 入力
def read_data():
    N_ = int(input())
    L_ = list(map(int, input().split()))
    return N_, L_

#探索
def binarySearch(N :int, L):
    ans = 0
    L.sort()
    # a,b は固定する
    for a_index in range(N):
        for b_index in range(a_index + 1, N):
            sum_of_a_and_b = L[a_index] + L[b_index]
            # c の可動範囲の右端を求める
            c_right_index = bisect.bisect_left(L, sum_of_a_and_b)
            # c の可動範囲は[b_index + 1, c_right_index) 右端が)となっているので-1している
            ans += max(0, c_right_index - b_index - 1)
    print(ans)

N, L = read_data()
binarySearch(N, L)