LCA offline

Initially you are given a tree consisting of only one root (the vertex with the number 1). You need to answer the following queries:

• ADD a b - hang the vertex b under the vertex a (it is guaranteed that the vertex a already exists).

• GET a b - return the LCA of vertices a and b.

The vertices are numbered from 1 to n. At each moment of time you have only one tree.

Input

The first line contains the number of queries k. Next k lines contains the queries. There is no more than 500000 queries of each type.

Output

For each query of type GET print in separate line one integer - the answer to the corresponding query.

Examples