Iahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees.

The game is played on a tree having $*n*$ nodes, numbered from $1$ to $*n*$. Each node $*i*$ has an initial value $*init*_{*i*}$, which is either 0 or 1. The root of the tree is node 1.

One can perform several (possibly, zero) operations on the tree during the game. The only available type of operation is to pick a node $*x*$. Right after someone has picked node $*x*$, the value of node $*x*$ flips, the values of sons of $*x*$ remain the same, the values of sons of sons of $*x*$ flips, the values of sons of sons of sons of $*x*$ remain the same and so on.

The goal of the game is to get each node $*i*$ to have value $*goal*_{*i*}$, which can also be only 0 or 1. You need to reach the goal of the game by using minimum number of operations.

Input

The first line contains an integer $*n*$ ($1 ≤ *n* ≤ 10^{5}$). Each of the next $*n* - 1$ lines contains two integers $*u*_{*i*}$ and $*v*_{*i*}$ ($1 ≤ *u*_{*i*}, *v*_{*i*} ≤ *n*$; $*u*_{*i*} ≠ *v*_{*i*}$) meaning there is an edge between nodes $*u*_{*i*}$ and $*v*_{*i*}$.

The next line contains $*n*$ integer numbers, the $*i*$-th of them corresponds to $*init*_{*i*}$ ($*init*_{*i*}$ is either 0 or 1). The following line also contains $*n*$ integer numbers, the $*i*$-th number corresponds to $*goal*_{*i*}$ ($*goal*_{*i*}$ is either 0 or 1).

Output

In the first line output an integer number $*cnt*$, representing the minimal number of operations you perform. Each of the next $*cnt*$ lines should contain an integer $*x*_{*i*}$, representing that you pick a node $*x*_{*i*}$.