CF983E NN country

Description

In the NN country, there are $ n $ cities, numbered from $ 1 $ to $ n $ , and $ n - 1 $ roads, connecting them. There is a roads path between any two cities. There are $ m $ bidirectional bus routes between cities. Buses drive between two cities taking the shortest path with stops in every city they drive through. Travelling by bus, you can travel from any stop on the route to any other. You can travel between cities only by bus. You are interested in $ q $ questions: is it possible to get from one city to another and what is the minimum number of buses you need to use for it?

Input Format

N/A

Output Format

N/A

Explanation/Hint

![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF983E/c42b59e68a69956240c890e5363c8c983d1d430c.png) Routes for first sample are marked on the picture.