B'Gildong was hiking a mountain, walking by millions of trees. Inspired by them, he suddenly came up with an interesting idea for trees in data structures: What if we add another edge in a tree? Then he found that such tree-like graphs are called 1-trees. Since Gildong was bored of solving too many tree problems, he wanted to see if similar techniques in trees can be used in 1-trees as well. Instead of solving it by himself, he 's going to test you by providing queries on 1-trees. First, he 'll provide you a tree (not 1-tree) with n vertices, then he will ask you q queries. Each query contains 5 integers: x , y , a , b , and k . This means you 're asked to determine if there exists a path from vertex a to b that contains exactly k edges after adding a bidirectional edge between vertices x and y . A path can contain the same vertices and same edges multiple times. All queries are independent of each other; i.e. the added edge in a query is removed in the next query. The first line contains an integer n ( 3 <= n <= 10^5 ), the number of vertices of the tree. Next n-1 lines contain two integers u and v ( 1 <= u,v <= n , u ne v ) each, which means there is an edge between vertex u and v . All edges are bidirectional and distinct. Next line contains an integer q ( 1 <= q <= 10^5 ), the number of queries Gildong wants to ask. Next q lines contain five integers x , y , a , b , and k each ( 1 <= x,y,a,b <= n , x ne y , 1 <= k <= 10^9 ) xe2 x80 x93 the integers explained in the description. It is guaranteed that the edge between x and y does not exist in the original tree. For each query, print "YES" if there exists a path that contains exactly k edges from vertex a to b after adding an edge between vertices x and y . Otherwise, print "NO". You can prin'...