CF852I Dating

This story is happening in a town named BubbleLand. There are $ n $ houses in BubbleLand. In each of these $ n $ houses lives a boy or a girl. People there really love numbers and everyone has their favorite number $ f $ . That means that the boy or girl that lives in the $ i $ -th house has favorite number equal to $ f_{i} $ . The houses are numerated with numbers $ 1 $ to $ n $ . The houses are connected with $ n-1 $ bidirectional roads and you can travel from any house to any other house in the town. There is exactly one path between every pair of houses. A new dating had agency opened their offices in this mysterious town and the citizens were very excited. They immediately sent $ q $ questions to the agency and each question was of the following format: - $ a\ b $ — asking how many ways are there to choose a couple (boy and girl) that have the same favorite number and live in one of the houses on the unique path from house $ a $ to house $ b $ . Help the dating agency to answer the questions and grow their business.

The first line contains an integer $ n $ ( $ 1

For each of the $ q $ questions output a single number, the answer to the citizens question.

In the first question from house $ 1 $ to house $ 3 $ , the potential couples are $ (1,3) $ and $ (6,3) $ . In the second question from house $ 7 $ to house $ 5 $ , the potential couples are $ (7,6) $ , $ (4,2) $ and $ (4,5) $ .