CF429A Xor-tree

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.

The first line contains an integer $ n $ ( $ 1

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} $ .