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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

const int maxn = 1000 + 50;
const int inf = 0x3f3f3f3f;

template < typename T >
void Read( T & x ){
	x=0;
	char ch;
	for( ch = getchar() ; ch < '0' || ch > '9' ; ch = getchar() );
	for( ; ch <= '9' && ch >= '0' ; ch = getchar() ) x = x * 10 + ch - '0';
}


int n , f[1001][5005] , x[maxn] , g[5005] , temp[5005];
vector < int > Edge[maxn];

void Dfs( int u ){
	for(auto && v : Edge[u])
		Dfs( v );
	memset( g , 0x3f , sizeof( g ) );
	g[0] = 0;
	for(auto && v : Edge[u]){
		memset( temp , 0x3f , sizeof( temp ) );
		for(int i = 0 ; i <= 5000 ; ++ i)
			if( g[i] <= 5000 )
				for(int j = 0 ; j + i <= 5000 ; ++ j)
					if( f[v][j] + g[i] <= 5000 )
						temp[i + j] = min( temp[i + j] , g[i] + f[v][j] );
		memcpy( g , temp , 5001 << 2 );
	}
	memset( temp , 0x3f , sizeof( temp ) );
	for(int i = 0 ; i <= 5000 ; ++ i)
		if( g[i] != inf ){
			if( i <= x[u] ) temp[x[u]] = min( temp[x[u]] , g[i] );
			if( g[i] <= x[u] ) temp[i] = min( temp[i] , x[u] );
		}
	memcpy( f[u] , temp , 5001 << 2 );
}

int main( int argc , char * argv[] ){
	Read( n );
	for(int i = 2 ; i <= n ; ++ i){
		int fa;
		Read( fa );
		Edge[fa].emplace_back( i );
	}
	for(int i = 1 ; i <= n ; ++ i) Read( x[i] );
	Dfs( 1 );
	for(int i = 0 ; i <= 5000 ; ++ i)
		if( f[1][i] != inf ){
			puts( "POSSIBLE" );
			return 0;
		}
	puts( "IMPOSSIBLE" );
	return 0;
}