{"raw_statement":[{"iden":"problem statement","content":"There is a tree with $N$ vertices, numbered $1$ through $N$. The $i$\\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$.\nCurrently, there are $A_i$ stones placed on vertex $i$. Determine whether it is possible to remove all the stones from the vertices by repeatedly performing the following operation:\n\n*   Select a pair of different leaves. Then, remove exactly one stone from every vertex on the path between those two vertices. Here, a _leaf_ is a vertex of the tree whose degree is $1$, and the selected leaves themselves are also considered as vertices on the path connecting them.\n\nNote that the operation cannot be performed if there is a vertex with no stone on the path."},{"iden":"constraints","content":"*   $2 ≦ N ≦ 10^5$\n*   $1 ≦ a_i,b_i ≦ N$\n*   $0 ≦ A_i ≦ 10^9$\n*   The given graph is a tree."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ … $A_N$\n$a_1$ $b_1$\n:\n$a_{N-1}$ $b_{N-1}$"},{"iden":"sample input 1","content":"5\n1 2 1 1 2\n2 4\n5 2\n3 2\n1 3"},{"iden":"sample output 1","content":"YES\n\nAll the stones can be removed, as follows:\n\n*   Select vertices $4$ and $5$. Then, there is one stone remaining on each vertex except $4$.\n*   Select vertices $1$ and $5$. Then, there is no stone on any vertex."},{"iden":"sample input 2","content":"3\n1 2 1\n1 2\n2 3"},{"iden":"sample output 2","content":"NO"},{"iden":"sample input 3","content":"6\n3 2 2 2 2 2\n1 2\n2 3\n1 4\n1 5\n4 6"},{"iden":"sample output 3","content":"YES"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}