AT_past202209_k 連結チェック

There is an undirected graph with $ N $ vertices and $ M $ edges. Initially, the $ i $ -th edge connects Vertex $ a_i $ and Vertex $ b_i $ . Process $ Q $ queries. The $ i $ -th query is represented by $ t_i $ , $ x_i $ , and $ y_i $ as follows. - If $ t_i=1 $ , add an edge connecting Vertex $ x_i $ and Vertex $ y_i $ . There are at most $ 10 $ queries of this kind in a single test case. - If $ t_i=2 $ , delete the edge connecting Vertex $ x_i $ and Vertex $ y_i $ . - If $ t_i=3 $ , print `Yes` if Vertex $ x_i $ and Vertex $ y_i $ belong to the same connected component, and `No` otherwise.

Input is given from Standard Input in the following format: > $ N $ $ M $ $ a_1 $ $ b_1 $ $ \vdots $ $ a_M $ $ b_M $ $ Q $ $ t_1 $ $ x_1 $ $ y_1 $ $ \vdots $ $ t_Q $ $ x_Q $ $ y_Q $

For each query such that $ t_i=3 $ , print the answer and then a newline.

### Sample Explanation 2 There may be no query such that $ t_i=3 $ . ### Constraints - $ 1 \leq N,M,Q \leq 10^5 $ - $ 1 \leq a_i \lt b_i \leq N $ - $ (a_i,b_i) \neq (a_j,b_j) $ if $ i \neq j $ . - $ t_i \in \{ 1,2,3 \} $ - $ 1 \leq x_i \lt y_i \leq N $ - There are at most $ 10 $ indices $ i $ such that $ t_i=1 $ . - If $ t_i=1 $ , there is no edge connecting Vertex $ x_i $ and Vertex $ y_i $ when the query is given. - If $ t_i=2 $ , there is an edge connecting Vertex $ x_i $ and Vertex $ y_i $ when the query is given. - All values in input are integers.