CF772B.Volatile Kite

You are given a convex polygon P with n distinct vertices _p_1, _p_2, ..., p__n. Vertex p__i has coordinates (x__i, y__i) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

给定一个具有 $n$ 个互异顶点 $p_1,\,p_2,\,\dots,\,p_n$ 的凸多边形 $P$。顶点 $p_i$ 在二维平面上的坐标为 $(x_i,\,y_i)$。这些顶点按顺时针顺序列出。

你可以选择一个实数 $D$，并将多边形的每个顶点移动至多距离 $D$（即移动后的顶点与原位置之间的欧氏距离不超过 $D$）。

求最大的 $D$ 值，使得无论你如何移动各顶点（只要满足移动距离不超过 $D$），该多边形均不自交且始终保持凸性。

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers x__i and y__i ( - 109 ≤ x__i, y__i ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

第一行包含一个整数 $n$（$4 \leq n \leq 1\,000$）—— 表示顶点的数量。

接下来的 $n$ 行包含各顶点的坐标。第 $i$ 行包含两个整数 $x_i$ 和 $y_i$（$-10^9 \leq x_i, y_i \leq 10^9$）—— 表示第 $i$ 个顶点的坐标。这些点保证按顺时针顺序给出，并构成一个严格凸多边形（特别地，任意三个连续的点不共线）。

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if .

输出一个实数 $D$，该实数为满足以下条件的最大实数：无论顶点如何移动，该多边形始终保持凸性。

若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

即，假设你的答案为 $a$，评测组的标准答案为 $b$。当且仅当 时，评测程序将判定你的答案正确。

Here is a picture of the first sample

Here is an example of making the polygon non-convex.

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

以下是第一个样例的示意图：

以下是一个使该多边形变为非凸多边形的示例：

该方案并非最优解，因为此时某一点的最大移动距离约为 0.4242640687，而我们实际上可以仅将每个点移动至多约为 0.3535533906 的距离，即可使其变为非凸多边形。