CF75E.Ship's Shortest Path

You have got a new job, and it's very interesting, you are a ship captain. Your first task is to move your ship from one point to another point, and for sure you want to move it at the minimum cost.

And it's well known that the shortest distance between any 2 points is the length of the line segment between these 2 points. But unfortunately there is an island in the sea, so sometimes you won't be able to move your ship in the line segment between the 2 points.

You can only move to safe points. A point is called safe if it's on the line segment between the start and end points, or if it's on the island's edge.

But you are too lucky, you have got some clever and strong workers and they can help you in your trip, they can help you move the ship in the sea and they will take 1 Egyptian pound for each moving unit in the sea, and they can carry the ship (yes, they are very strong) and walk on the island and they will take 2 Egyptian pounds for each moving unit in the island. The money which you will give to them will be divided between all workers, so the number of workers does not matter here.

You can move your ship on the island edge, and it will be considered moving in the sea.

Now you have a sea map, and you have to decide what is the minimum cost for your trip.

Your starting point is (xStart, yStart), and the end point is (xEnd, yEnd), both points will be different.

The island will be a convex polygon and there will be no more than 2 polygon points on the same line, also the starting and the end points won't be inside or on the boundary of the island. The points for the polygon will be given in the anti-clockwise order.

你获得了一份新工作，而且这份工作非常有趣——你成了一名船长。你的第一项任务是将船从一个点移动到另一个点，当然，你希望以最低成本完成这次航行。

众所周知，任意两点之间的最短距离即为连接这两点的线段长度。但不幸的是，海中有一座岛屿，因此有时你无法直接沿起点与终点之间的线段航行。

你只能移动到“安全点”。一个点被称为安全点，当且仅当它位于起点与终点之间的线段上，或位于岛屿的边界上。

但你非常幸运，拥有一些聪明而强壮的工人，他们能在旅途中为你提供帮助：他们可以在海上推动船只，每在海上移动一个单位距离需支付 1 埃及镑；他们也可以扛着船（是的，他们非常强壮）在岛上行走，每在岛上移动一个单位距离需支付 2 埃及镑。你支付给他们的总金额将在所有工人之间均分，因此工人的具体人数在此问题中无关紧要。

你可以在岛屿的边界上移动船只，此时该移动被视为在海上进行。

现在你手上有一张海图，你需要确定此次航行的最低成本。

你的起始点为 $(x_{\text{Start}}, y_{\text{Start}})$，终点为 $(x_{\text{End}}, y_{\text{End}})$，这两个点互不相同。

岛屿是一个凸多边形，且任意一条直线上至多有两个多边形顶点；此外，起点和终点均不在岛屿内部或其边界上。多边形的顶点按逆时针顺序给出。

The first line contains 4 integers, xStart, yStart, xEnd and yEnd ( - 100 ≤ xStart, yStart, xEnd, yEnd ≤ 100). The second line contains an integer n, which is the number of points in the polygon (3 ≤ n ≤ 30), followed by a line containing n pairs of integers x and y, which are the coordinates of the points ( - 100 ≤ x, y ≤ 100), the polygon points will be distinct.

第一行包含 4 个整数：$xStart$、$yStart$、$xEnd$ 和 $yEnd$（满足 $-100 \le xStart,\ yStart,\ xEnd,\ yEnd \le 100$）。
第二行包含一个整数 $n$，表示多边形的顶点个数（$3 \le n \le 30$）；随后一行包含 $n$ 对整数 $x$ 和 $y$，即各顶点的坐标（满足 $-100 \le x,\ y \le 100$），且所有多边形顶点互不相同。

Print one line which contains the minimum possible cost. The absolute or relative error in the answer should not exceed 10 - 6.

输出一行，包含最小可能的花费。答案的绝对或相对误差不应超过 $10^{-6}$。