Problem:
Score : 700 points

Problem Statement

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}

Output

If it is possible to remove all the stones from the vertices, print YES. Otherwise, print NO.

Sample Input 1

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

Sample 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.

Sample Input 2

3
1 2 1
1 2
2 3

Sample Output 2

NO

Sample Input 3

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

Sample Output 3

YES

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

N = gets.to_i
as = gets.split.map(&:to_i)
edges = Array.new(N){{}}
(N-1).times do
    a, b = gets.split.map(&:to_i)
    edges[a-1][b-1] = true
    edges[b-1][a-1] = true
end

start = N.times.find{|i|edges[i].length > 1}
stack = [start]
visited = []
visited[start] = true
bottomup = Array.new(N){Array.new}
while stack.length > 0
    updated = false
    s = stack[-1]
    edges[s].each do |t, _|
        next if visited[t]
        stack.push(t)
        visited[t] = true
        updated = true
        break
    end
    unless updated
        if bottomup[s].length == 0
            bottomup[stack[-2]].push(as[s])
        else
            bu = bottomup[s]
            sum = bu.inject(:+)
            limit = 2*bu.max - sum
            uplink = 2*as[s] - sum
            if limit > uplink || uplink < 0 || (s == start && uplink != 0)
                puts 'NO'
                exit
            end
            bottomup[stack[-2]].push(uplink) if stack.length > 1
        end
        stack.pop
    end
end
puts 'YES'