Problem:
Score : 700 points

Problem Statement

We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 \leq i \leq N) is Vertex P_i.

To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.

Snuke has a favorite integer sequence, X_1, X_2, ..., X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.

The total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.

Here, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.

Determine whether it is possible to allocate colors and weights in this way.

Constraints

1 \leq N \leq 1 000

1 \leq P_i \leq i - 1

0 \leq X_i \leq 5 000

Inputs

Input is given from Standard Input in the following format:

N
P_2 P_3 ... P_N
X_1 X_2 ... X_N

Outputs

If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3
1 1
4 3 2

Sample Output 1

POSSIBLE

For example, the following allocation satisfies the condition:

Set the color of Vertex 1 to white and its weight to 2.

Set the color of Vertex 2 to black and its weight to 3.

Set the color of Vertex 3 to white and its weight to 2.

There are also other possible allocations.

Sample Input 2

3
1 2
1 2 3

Sample Output 2

IMPOSSIBLE

If the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.

If different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.

Thus, there exists no allocation of colors and weights that satisfies the condition.

Sample Input 3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Sample Output 3

POSSIBLE

Sample Input 4

1

0

Sample Output 4

POSSIBLE

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n=gets.to_i
if n<3 then
    puts "POSSIBLE"
    exit(0)
end
p=gets.split(" ").map{|i|i.to_i-1}
p.unshift 0
x=gets.split(" ").map(&:to_i)
edge=Array.new(n){[]}
isLeaf=Array.new(n,true)
sum=Array.new(n,0)
n.times{|i|
    isLeaf[p[i]]=false
    if p[i]!=i then
        edge[p[i]].<<i
    end
}
[*0...n].reverse_each{|i|
    if isLeaf[i] then
        sum[i]=x[i]
        next
    end
    edge[i].each{|from|
        sum[i]+=sum[from]
    }
    dp=Array.new(x[i]+1,false)
    dp2=Array.new(x[i]+1,false)
    dp[0]=true
    edge[i].each{|from|
        a=x[from]
        b=sum[from]-x[from]
        [*0..x[i]].reverse_each{|j|
            if !dp[j] then
                next
            end
            if j+a<=x[i] then
                dp2[j+a]=true
            end
            if j+b<=x[i] then
                dp2[j+b]=true
            end
        }
        dp=dp2
        dp2=Array.new(x[i]+1,false)
    }
    black=-1
    [*0..x[i]].reverse_each{|j|
        if dp[j] then
            black=j
            break
        end
    }
    if black==-1 then
        puts "IMPOSSIBLE"
        exit(0)
    end
    sum[i]=sum[i]-black+x[i]
}
puts "POSSIBLE"