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C. Xor-tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub 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}.

Examples

Input

10

2 1

3 1

4 2

5 1

6 2

7 5

8 6

9 8

10 5

1 0 1 1 0 1 0 1 0 1

1 0 1 0 0 1 1 1 0 1

Output

2

4

7

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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