# 算法分析与设计习题 (参考)

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 $N$ ($1 \le N \le 1~000$) farms (conveniently numbered $1$..$N$) is represented by a position $(X_i, Y_i)$ on the plane ($0 \le X_i \le 1~000~000$, $0 \le Y_i \le 1~000~000$). Given the preexisting $M$ roads ($1 \le M \le 1~000$) as pairs of connected farms, help Farmer John determine the smallest length of additional roads he must build to connect all his farms.

### 输入格式

• Line $1$: Two space-separated integers: $N$ and $M$
• Lines $2$..$N+1$: Two space-separated integers: $X_i$ and $Y_i$
• 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 $j$.

### 输出格式

• Line $1$: Smallest length of additional roads required to connect allfarms, printed without rounding to two decimal places. Be sure to calculate distances as 64-bit floating point numbers.

### 样例

Input
4 1
1 1
3 1
2 3
4 3
1 4

Output
4.00


### 提示

INPUT DETAILS:

Four farms at locations (1,1), (3,1), (2,3), and (4,3). Farms 1 and 4 are connected by a road.

OUTPUT DETAILS:

Connect farms 1 and 2 with a road that is 2.00 units long, then connect farms 3 and 4 with a road that is 2.00 units long. This is the best we can do, and gives us a total of 4.00 unit lengths.