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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
from itertools import combinations 
def main():
    N = int(readline())
    L = [int(i) for i in readline().split()]

    #ソートしておく
    L.sort()

    #最長以外の二辺を先に決める
    #インデックスで二辺を選ぶ。最長の辺はjよりインデックスが大きいものとなることが保証される
    #jより後ろでc<a+bとなる最長の辺cの数を求めれば良い。二分探索で条件を満たす最大の辺を見つけるとよい

    #インデックス用の値を用意
    p = [i for i in range(N)]

    #組みを作る
    idxPairs = [(i, j) for i,j in combinations(p, 2)]

    #jよりインデックスが大きい辺の中から最長の辺を見つける
    ans = 0
    for i, j in idxPairs:
        #j以降を二分探索で調べる
        #最長の辺をL[j]と選ぶと必ず三角形を作ることができる
        l = j
        r = N 
        while r-l>1:
            mid = (r+l)//2
            if L[mid] < L[i]+L[j]:
                l = mid
            else:
                r = mid
        ans += l-j
    print(ans)
if __name__ == '__main__':
    main()