You are given a connected simple undirected graph $G$ with $N$ vertices numbered $1$ to $N$ and $N$ edges. The $i$\-th edge connects Vertex $u_i$ and Vertex $v_i$ bidirectionally. Answer the following $Q$ queries. - Determine whether there is a unique simple path from Vertex $x_i$ to Vertex $y_i$ (a simple path is a path without repetition of vertices). ### Constraints - $3 \leq N \leq 2 \times 10^5$ - $1 \leq u_i < v_i\leq N$ - $(u_i,v_i) \neq (u_j,v_j)$ if $i \neq j$. - $G$ is a connected simple undirected graph with $N$ vertices and $N$ edges. - $1 \leq Q \leq 2 \times 10^5$ - $1 \leq x_i < y_i\leq N$ - All values in input are integers.

Input is given from Standard Input in the following format: $N$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_N$ $v_N$ $Q$ $x_1$ $y_1$ $x_2$ $y_2$ $\vdots$ $x_Q$ $y_Q$

Print $Q$ lines. The $i$\-th line $(1 \leq i \leq Q)$ should contain `Yes` if there is a unique simple path from Vertex $x_i$ to Vertex $y_i$, and `No` otherwise.