27430번 - Gossips 다국어

문제

Poli is in her first year at college. Although she went to one of the best universities she quickly discovered that her colleagues are split into N friendship groups, the main purpose of these groups being spreading gossips. Poli knows that each group i is formed out of one or more subgroups so that each subgroup can be a part of only one group. Now, let's say that a group i finds a gossip about group j; then all the subgroups of i (and the subgroups of these subgroups etc.) and all the groups of which group i is a part of know the gossip about group j. Also all of these groups know the gossip about every group of which group j is a part of (but they don't know anything about the subgroups of j, because those members may not be implicated in the gossip).

Because Poli is a friend with every one of her colleagues she knows when a gossip appears (that is when a group i finds a gossip about a group j). Now she wants to be able to answer fast to questions like: << Does a group i know a gossip about group j? >>.

Unfortunately Poli's college is rather big, so you have to help her!

입력

On the first line of the standard input there are three numbers N - the number of groups, M - the number of relations between the groups and Q - the number of queries. Next there are M lines of the form a b representing that group b is a subgroup of group a. The next Q lines have three numbers each: s - the type of query, and x y - two groups. If s is 1 then you have to answer YES if there is at least one gossips between group x and group y or NO if not. If s is 2 then group x just found out a gossip about group y.

출력

You must print to the standard output several lines, one for each query of type 1, each line being YES or NO (without quotation marks).

제한

• 1 ≤ N, Q ≤ 100,000
• 1 ≤ M < N
• 1 ≤ x, y ≤ N
• if a group i knows a gossip about group j it doesn't mean that group j knows also a gossip about i.

힌트