2 
-------------
2 
3 
-------------
2 
3 
2 
-------------
2 
3 2 3 
-------------
2 
3 2 3 
5 
-------------
2 
3 2 3 
5 
6 
-------------
2 
3 2 3 
5 
6 
7 
-------------
2 
3 2 3 
5 
6 
7 
8 
-------------
YES
3 1 1 2 5 6 7