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constructive algorithms

dfs and similar

trees

*2300

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C. Bear and Drawing

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLimak 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?

Input

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.

Output

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

Examples

Input

8

1 2

1 3

1 6

6 4

6 7

6 5

7 8

Output

Yes

Input

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

Output

No

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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