There are n vertices.

Your task is to perform q queries:

1 a b - add an undirected edge of the length 1 between vertices a and b

2 a - find the distance to the furthest vertex reachable from the vertex a

Guaranteed that graph will not contain loops and cycles during all the time.

$INPUT$

First line of the input contains two integers n and q $(1 \leq n \leq 10^5, 1 \leq q \leq 3 \cdot 10^5)$

Then follow q lines. The i-th of them contains integers: $type_i$ $(1 \leq type_i \leq 2)$, $a_i$ $(1 \leq a \leq n)$ and if $type_i = 1$ $b_i$ $(1 \leq b_i \leq n)$.

$OUTPUT$

Print the distance which is needed for each query of the second type.