Codeforces 573C Bear and Drawing

Limak is a little bear who learns to draw. People usually start with houses, fences and flowers-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 and parallel rows of dots. Little Bear wants to assign vertices of a tree to some n distinct dots in a paper so that edges would interse CT only at their endpoints-drawn tree must is planar. Below you can see one of correct drawings for the first sample test.

Is it possible-Limak to draw chosen tree?

Input

The first line contains a single integer n (1≤ n ≤105).

Next N -1 lines contain description of a tree. i-th of them contains II space-separated integers ai and b i (1≤ ai, bi ≤ n, a i ≠ bi) denoting an edge between vertices ai and c30>bi. 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).

Sample Test (s) 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

Exercises

Codeforces 573C Bear and Drawing