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:
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.
For each query of the second type print "Yes" if b can be reached from a and "No" otherwise.
Graph before change
Graph after change in the third query