Bear and Drawing

题意翻译

Limak是一只小熊，他想学画画。 对于画画，人们总是从常见的房屋、栅栏、花朵开始尝试—— 但是，作为住在森林里的熊，Limak决定从树开始画。 树是n个节点n-1条边的无向连通图。 Limak有无限长的纸条，纸条上有两排平行的点，点的数量也是无限的，如图显示了纸条的一部分。 Limak想要把这些点中的n个作为树上的点，**注意，所有边只能在顶点处相交，绘制的树必须在同一平面上。** 如图是一个合法的绘画范例。 现在给出树的结构，请你回答：Limak能够画出这棵树吗？ 输入包含了n(n<=100000)和n-1条边，保证为合法的树。 输出一行一个字符串，表示Limak是否能够画出这棵树，输出"Yes"或"No"（不包括引号）。

题目描述

Limak is a little bear who learns to draw. People usually start with houses, fences and flowers but why would bears do it? Limak lives in the forest and he decides to draw a tree. Recall that tree is a connected graph consisting of $ n $ vertices and $ n-1 $ edges. Limak chose a tree with $ n $ vertices. He has infinite strip of paper with two parallel rows of dots. Little bear wants to assign vertices of a tree to some $ n $ distinct dots on a paper so that edges would intersect only at their endpoints — drawn tree must be planar. Below you can see one of correct drawings for the first sample test. Is it possible for Limak to draw chosen tree?

输入输出格式

输入格式

The first line contains single integer $ n $ ( $ 1<=n<=10^{5} $ ). Next $ n-1 $ lines contain description of a tree. $ i $ -th of them contains two space-separated integers $ a_{i} $ and $ b_{i} $ ( $ 1<=a_{i},b_{i}<=n,a_{i}≠b_{i} $ ) denoting an edge between vertices $ a_{i} $ and $ b_{i} $ . It's guaranteed that given description forms a tree.

输出格式

Print "Yes" (without the quotes) if Limak can draw chosen tree. Otherwise, print "No" (without the quotes).

输入输出样例

输入样例 #1

8
1 2
1 3
1 6
6 4
6 7
6 5
7 8

输出样例 #1

Yes

输入样例 #2

13
1 2
1 3
1 4
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13

输出样例 #2

No