Cupboard and Balloons

### **题目描述** 一个名叫 Xenia 的女孩有一个从前面看起来像弧形的橱柜。这个弧形由一个半圆形顶部（半径为 $r$）和两个高度为 $h$ 的侧壁构成。橱柜的深度为 $r$，也就是说，从侧面看起来像一个底边为 $r$，高度为 $h+r$ 的矩形。下图显示了橱柜的外观（左侧是前视图，右侧是侧视图）。 Xenia 在她的生日上得到了很多气球。这个女孩讨厌凌乱，所以她想把气球存放在橱柜里。幸运的是，每个气球都是半径为 $\frac{r}{2}$ 的球体。帮助 Xenia 计算她可以放入橱柜的最大气球数量。 如果在左侧或右侧视图中看不到气球的任何部分，可以说一个气球在橱柜里。橱柜里的气球可以彼此接触。不允许挤压气球或以任何方式变形气球。可以假设橱柜的墙壁非常薄，可以忽略不计。 ### **输入格式** 读入两个整数 $r,h$ $(l\le r,h\le 10^7)$。 ### **输出格式** 输出一个整数表示最多能有多少个气球放进橱柜。

A girl named Xenia has a cupboard that looks like an arc from ahead. The arc is made of a semicircle with radius $ r $ (the cupboard's top) and two walls of height $ h $ (the cupboard's sides). The cupboard's depth is $ r $ , that is, it looks like a rectangle with base $ r $ and height $ h+r $ from the sides. The figure below shows what the cupboard looks like (the front view is on the left, the side view is on the right). Xenia got lots of balloons for her birthday. The girl hates the mess, so she wants to store the balloons in the cupboard. Luckily, each balloon is a sphere with radius . Help Xenia calculate the maximum number of balloons she can put in her cupboard. You can say that a balloon is in the cupboard if you can't see any part of the balloon on the left or right view. The balloons in the cupboard can touch each other. It is not allowed to squeeze the balloons or deform them in any way. You can assume that the cupboard's walls are negligibly thin.

The single line contains two integers $ r,h $ $ (1<=r,h<=10^{7}) $ .

Print a single integer — the maximum number of balloons Xenia can put in the cupboard.

1 1

3

1 2

5

2 1

2