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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main implements Runnable {
	public static void main(String[] args) throws FileNotFoundException {
		new Main().run2();
	}

	long[][] f;
	long INF = Integer.MAX_VALUE / 10;
	// f[i][0]={w[i],#黒}∧col[i]=白
	// f[i][1]={#白,w[i]}∧col[i]=黒

	void dfs(int cur, int par, ArrayList<Integer>[] g, int[] x) {
		for (int dst : g[cur]) {
			if (dst == par) {
				continue;
			}
			dfs(dst, cur, g, x);
			// col[cur]=黒
			{
				long add = INF;
				if (x[dst] <= x[cur]) {// col[dst]=黒
					add = Math.min(add, f[dst][0]);
				}
				if (f[dst][1] <= x[cur]) {// col[dst]=白
					add = Math.min(add, x[dst]);
				}
				if (add < INF && f[cur][1] < INF)
					f[cur][1] += add;
				else
					f[cur][1] = INF;
			}
			// col[cur]=白
			{
				long add = INF;
				if (f[dst][0] <= x[cur]) {// col[dst]=黒
					add = Math.min(add, x[dst]);
				}
				if (x[dst] <= x[cur]) {// col[dst]=白
					add = Math.min(add, f[dst][1]);
				}
				if (add < INF && f[cur][0] < INF)
					f[cur][0] += add;
				else
					f[cur][0] = INF;
			}
		}

	}

	// f[i][0]={w[i],#黒}∧col[i]=白
	// f[i][1]={#白,w[i]}∧col[i]=黒

	void solve(int n, int[] p, int[] x) {
		ArrayList<Integer>[] g = new ArrayList[n];
		for (int i = 0; i < n; ++i)
			g[i] = new ArrayList<>();
		for (int i = 0; i < n - 1; ++i) {
			g[i + 1].add(p[i]);
			g[p[i]].add(i + 1);
		}
		f = new long[n][2];
		dfs(0, -1, g, x);
		if (f[0][0] < INF || f[0][1] < INF) {
			System.out.println("POSSIBLE");
		} else {
			System.out.println("IMPOSSIBLE");
		}
	}

	public void run() {
		new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start();
	}

	void run2() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] p = new int[n];
		int[] x = new int[n];
		for (int i = 0; i < n - 1; ++i) {
			p[i] = sc.nextInt();
			--p[i];
		}
		for (int i = 0; i < n; ++i) {
			x[i] = sc.nextInt();
		}

		solve(n, p, x);
	}

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}