CF1661F.Teleporters

There are $n+1$ teleporters on a straight line, located in points $0$, $a_1$, $a_2$, $a_3$, ..., $a_n$. It's possible to teleport from point $x$ to point $y$ if there are teleporters in both of those points, and it costs $(x-y)^2$ energy.

You want to install some additional teleporters so that it is possible to get from the point $0$ to the point $a_n$ (possibly through some other teleporters) spending no more than $m$ energy in total. Each teleporter you install must be located in an integer point.

What is the minimum number of teleporters you have to install?

一条直线上有 $n+1$ 个传送器，位置分别为 $0$、$a_1$、$a_2$、$a_3$、...、$a_n$。若点 $x$ 和点 $y$ 处均存在传送器，则可以从 $x$ 传送到 $y$，消耗能量为 $(x-y)^2$。

你希望安装若干额外的传送器，使得能够从点 $0$ 到达点 $a_n$（可能经过其他传送器），且总消耗能量不超过 $m$。你安装的每个传送器必须位于整数坐标处。

问：最少需要安装多少个传送器？

The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_1 \lt a_2 \lt a_3 \lt \dots \lt a_n \le 10^9$).

The third line contains one integer $m$ ($a_n \le m \le 10^{18}$).

第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_1 \lt a_2 \lt a_3 \lt \dots \lt a_n \le 10^9$）。

第三行包含一个整数 $m$（$a_n \le m \le 10^{18}$）。

Print one integer — the minimum number of teleporters you have to install so that it is possible to get from $0$ to $a_n$ spending at most $m$ energy. It can be shown that it's always possible under the constraints from the input format.

输出一个整数——为使从 $0$ 到达 $a_n$ 所消耗的能量至多为 $m$，所需安装的传送器的最少数量。在题目给定的输入约束下，总存在可行解。