Cleaning

AtCoder

IDagc010_c

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices, numbered $1$ through $N$. The $i$\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$. Currently, 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: * 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. Note that the operation cannot be performed if there is a vertex with no stone on the path. ## Constraints * $2 ≦ N ≦ 10^5$ * $1 ≦ a_i,b_i ≦ N$ * $0 ≦ A_i ≦ 10^9$ * The given graph is a tree. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ … $A_N$ $a_1$ $b_1$ : $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

YES

All the stones can be removed, as follows:

*   Select vertices $4$ and $5$. Then, there is one stone remaining on each vertex except $4$.
*   Select vertices $1$ and $5$. Then, there is no stone on any vertex.

Input #2

Output #2

NO

Input #3

6
3 2 2 2 2 2
1 2
2 3
1 4
1 5
4 6

Output #3

YES

API Response (JSON)

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