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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define f1(a,b,c) for(int c=a;c<=b;c++)
#define f2(a,b,c) for(int c=a;c>=b;c--)
#define f3(a,b,c) for(int c=a;c;c=b)
#define so1(a,n) sort(a+1,a+n+1,mycmp);
#define so2(a,n) sort(a+1,a+n+1);
#define ll long long
#define itn int
#define ubt int 
#define mp make_pair
#define pii pair<int,int>
#define pll pair<ll,ll>
const int twx=5e3+100;
const int inf=0x3f3f3f3f;
ll read()
{
    ll sum=0;
    ll flag=1;
    char c=getchar();
    while(c<'0'||c>'9')
    {
        if(c=='-')
        {
            flag=-1;
        }
        c=getchar();
    }
    while(c>='0'&&c<='9')
    {
        sum=((sum*10)+c-'0');
        c=getchar();
    }
    return sum*flag;
}
int n;
int xs[twx];
struct LV
{
    int y;
    int Next;
}a[twx];
int Link[twx];
int len;
int asd[twx];
int qwe[2][twx];
void Insert(int x,int y)
{
    a[++len].y=y;
    a[len].Next=Link[x];
    Link[x]=len;
}
void dfs(int x)
{
    f3(Link[x],a[i].Next,i)
    {
        int y=a[i].y;
        dfs(y);
    }
    memset(qwe[0],0x3f,sizeof qwe[0]);
    int tmp=0;
    qwe[tmp][0]=0;
    f3(Link[x],a[i].Next,i)
    {
        int y=a[i].y;
        tmp^=1;
        memset(qwe[tmp],0x3f,sizeof qwe[tmp]);
        f1(0,xs[x],j)
        {
            if(j-xs[y]>=0)
            {
                qwe[tmp][j]=min(qwe[tmp][j],qwe[tmp^1][j-xs[y]]+asd[y]);
            }
            if(j-asd[y]>=0)
            {
                qwe[tmp][j]=min(qwe[tmp][j],qwe[tmp^1][j-asd[y]]+xs[y]);
            }
        }
    }
    f1(0,xs[x],i)
    {
        asd[x]=min(asd[x],qwe[tmp][i]);
    }
}
void init()
{
	n=read();
    f1(2,n,i)
    {
        int p=read();
        Insert(p,i);
    }
    f1(1,n,i)
    {
        xs[i]=read();
    }
    memset(asd,0x3f,sizeof asd);
    dfs(1);
    if(asd[1]!=inf)
    {
        puts("POSSIBLE");
    }
    else
    {
        puts("IMPOSSIBLE");
    }
}
int main()
{
    init();
	return 0;
}