Teleporters
Description
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?
The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_1 < a_2 < a_3 < \dots < a_n \le 10^9$).
The third line contains one integer $m$ ($a_n \le m \le 10^{18}$).
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.
Input
The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_1 < a_2 < a_3 < \dots < a_n \le 10^9$).
The third line contains one integer $m$ ($a_n \le m \le 10^{18}$).
Output
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.
Samples
2
1 5
7
2
2
1 5
6
3
1
5
5
4
1
1000000000
1000000043
999999978