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.