## 题目描述

Farmer John had just acquired several new farms! He wants to connect the farms with roads so that he can travel from any farm to any other farm via a sequence of roads; roads already connect some of the farms. Each of the N (1 ≤ N ≤ 1,000) farms (conveniently numbered 1..N) is represented by a position (Xi, Yi) on the plane (0 ≤ Xi ≤ 1,000,000; 0 ≤ Yi ≤ 1,000,000). Given the preexisting M roads (1 ≤ M ≤ 1,000) as pairs of connected farms, help Farmer John determine the smallest length of additional roads he must build to connect all his farms. 给定 \$n\$ 个点的坐标，第 \$i\$ 个点的坐标为 \$(x_i,y_i)\$，这 \$n\$ 个点编号为 \$1\$ 到 \$n\$。给定 \$m\$ 条边，第 \$i\$ 条边连接第 \$u_i\$ 个点和第 \$v_i\$ 个点。现在要求你添加一些边，并且能使得任意一点都可以连通其他所有点。求添加的边的总长度的最小值。

## 输入输出格式

### 输入格式

\* Line 1: Two space-separated integers: N and M \* Lines 2..N+1: Two space-separated integers: Xi and Yi \* Lines N+2..N+M+2: Two space-separated integers: i and j, indicating that there is already a road connecting the farm i and farm j. 第一行两个整数 \$n,m\$ 代表点数与边数。 接下来 \$n\$ 行每行两个整数 \$x_i,y_i\$ 代表第 \$i\$ 个点的坐标。 接下来 \$m\$ 行每行两个整数 \$u_i,v_i\$ 代表第 \$i\$ 条边连接第 \$u_i\$ 个点和第 \$v_i\$ 个点。

### 输出格式

\* Line 1: Smallest length of additional roads required to connect all farms, printed without rounding to two decimal places. Be sure to calculate distances as 64-bit floating point numbers. 一行一个实数代表添加的边的最小长度，要求保留两位小数，为了避免误差， 请用 \$64\$ 位实型变量进行计算。

## 输入输出样例

### 输入样例 #1

``````4 1
1 1
3 1
2 3
4 3
1 4``````

### 输出样例 #1

``4.00``

## 说明

### 数据规模与约定 对于 \$100\%\$ 的整数，\$1 \le n,m \le 1000\$，\$1 \le x_i,y_i \le 10^6\$，\$1 \le u_i,v_i \le n\$。 ### 说明 Translated by 一只书虫仔。