A Tree Game
시간 제한1초메모리 제한2048 MB
모든 간선이 열린 트리에서 칩을 옮겨 차수가 1인 정점에 도달하려는 I와 매 라운드 간선 하나를 닫는 J의 승패를 판정한다.
문제
Little I and Little J are playing a game again.
Little J brings a tree with vertices. Each edge of the tree has two states: open and closed. Initially, all edges of the tree are open.
There is a chip initially placed at vertex . Little I can move the chip, and the goal is to move the chip to a vertex with degree exactly equal to . Little J can close edges of the tree with the goal of preventing Little I from moving the chip to a vertex with degree exactly . The degree of a vertex is the number of edges connected to it, regardless of whether they are open or closed.
The game consists of several rounds, each round having the following steps:
- Little I Task Determination: If the chip is at a vertex with degree exactly , Little I wins. Otherwise, proceed to step 2.
- Little J Action: Little J closes one currently open edge permanently. If there are no open edges at the moment, skip the action and proceed to step 3.
- Little I Action: Little I chooses an open edge connected to the vertex currently containing the chip, and moves the chip to the other end of this edge. If there is no such edge, Little J wins. Otherwise, a new round begins, going back to step 1.
Little J wants to know who will win if Little I and Little J know the structure of this tree and are extremely smart.
입력
The first line contains a single integer () representing the number of vertices in the tree.
Then follow lines, each containing two integers and () representing two vertices connected by an edge of the tree.
출력
If Little I wins, print 1. Otherwise, print 0.