Uneori îmi spun: am să mor
atât de singuratecă-n mijlocul lor;
limba simplă a bucuriilor n-am învâțat;
am să mor ca o pasăre care prea mult a zburat,
dar n-a făcut cuib nicăieri.

― Oamenii ma uimesc, Magda Isafost

As of writing the informal statement, the winter just came and the statement was in season. Now, it is not winter anymore, so here is the formal statement instead:

You are given a connected graph with N nodes and M edges. You are given Q queries of the following types:
$\texttt{1 u}$: Given node u (1 ≤ u ≤ N), set the state of the node u to frozen.
$\texttt{2 t}$: Given t, let t units of time pass by.
$\texttt{3 v}$: Given node v (1 ≤ v ≤ N), answer if node v is currently frozen.

Initially, no node is frozen.
The graph has the following property:
If, at time T, a node u is frozen, then, at time (T+1), all neighbours of u become frozen.

For each query of type 3, answer whether the node is currently frozen.

Note:
If a node is already frozen, it remains unaffected after a type 1 query.
If, for a frozen node u, a neighbour v of node u is frozen at time T, node v remains unaffected at time (T+1).

------ Input Format ------

• The first line of input contains three integers N, M, and Q.
• M lines follow, the i^{th} of which contains two integers u_{i} and v_{i}, representing there is an edge between nodes u_{i} and v_{i}.
• Then, Q lines follow, the j^{th} of which contains two integers type_{j} and x_{j}.
  If type_{j} is 1 or 2, it indicates that you must effectuate an update of the type type_{j} with parameter x_{j}. Otherwise, answer the query with parameter x_{j}

------ Output Format ------

For each query of type 3, print $\texttt{YES}$ if the queried node is frozen. Otherwise, print $\texttt{NO}$.

You may print each character of the string in uppercase or lowercase (for example, the strings $\texttt{YeS}, \texttt{yEs}, \texttt{yes}$ and $\texttt{YES}$ will all be treated as identical).

------ Constraints ------

$1 ≤N, Q ≤10^{5}$
$1 ≤M ≤3 \cdot 10^{5}$
$1 ≤u_{i}, v_{i} ≤N$
$1 ≤type_{j} ≤3$
$1 ≤x_{j} ≤N$, if the query type is $1$ or $3$.
$1 ≤x_{j} ≤10^{9}$, if the query type is $2$.

------ subtasks ------

Subtask 1 (10 points): $1 ≤N ≤1000, 1 ≤Q ≤2000, 1 ≤M ≤3000$.
Subtask 2 (30 points): Each node in the given graph has at most two neighbours.
Subtask 3 (60 points): Original constraints.

----- Sample Input 1 ------
6 6 6
1 2
2 3
4 1
5 4
6 1
6 5
1 1
3 1
1 5
2 1
3 4
3 3
----- Sample Output 1 ------
YES
YES
NO
----- explanation 1 ------
Test Case $1$: The graph looks like:

• Query $1$: Freeze the node $1$. The graph looks like:

• Query $2$: Find the status of node $1$. Since node $1$ is frozen, we print $\texttt{YES}$.

• Query $3$: Freeze the node $5$. The graph looks like:

• Query $4$: $1$ unit of time passes. Before this, nodes $1$ and $5$ were frozen.
  After $1$ second, all the neighbours of node $1$, i.e., nodes $2, 4,$ and $6$, and all the neighbours of node $5$, i.e., nodes $4$ and $6$ are frozen.
  Thus, after this query, the frozen nodes in the graph are $1, 2, 4, 5,$ and $6$. The graph looks like:

• Query $5$: Find the status of node $4$. Since node $4$ is frozen, we print $\texttt{YES}$.

• Query $6$: Find the status of node $3$. Since node $3$ is not frozen, we print $\texttt{NO}$.

见题面

见题面