Problem Description

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 $1 \sim N$) 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.

Input Format

• Line $1$: Two space-separated integers: $N$ and $M$.

• Lines $2 \sim N+1$: Two space-separated integers: $X_i$ and $Y_i$.

• Lines $N+2 \sim N+M+2$: Two space-separated integers: $i$ and $j$, indicating that there is already a road connecting the farm $i$ and farm $j$.

Output Format

• 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.

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

4.00