Alice has a wheel-graph: an undirected graph with \(n+1\) nodes and \(2 \cdot n\) edges. In wheel-graph there are edges between \(n + 1\) and i for each integer \(i : 1 \leq i \leq n\) and edges between i and \(i\mod n + 1\) for each integer \(i : 1 <= i <= n\) (see examples to understand it better). Undirected graphs are quite boring for Alice so she made a directed wheel-graph and now each edge has a direction.

Alice wants performs two types of queries:

• 1 a b - change orientation between nodes a and b. Now orientation is from a to b (before this query in graph was a edge from node b to node a).
• 2 a b - check if is b reachable from a.

Help her.

\(INPUT\)
The first line of the input contains a single integer n \((2 \leq n \leq 200 000)\) - number of nodes without center node.

Then follow \(n \cdot 2\) lines with edges description. The i-th of these lines contains two integers \(a_i\) and \(b_i\) - index of node the edge start from, index of node the edge goes to. It is guaranteed that edges formed a correct directed wheel-graph with \(n + 1\) nodes.

Next line of the input contains a single integer q \((1 \leq q \leq 200 000)\) - number of queries.

Then q lines follow with queries description. The i-th of these lines contains three integers \(type_i\), \(a_i\), \(b_i\) - parameters of the i-th query.

\(OUTPUT\)
For each query of the second type print "Yes" if b can be reached from a and "No" otherwise.