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 <cstdio>
#include <iostream>
#include <cmath>
#include <cstring>
#include <sstream>
#include <algorithm>
#include <cstdlib>
#include <map>
#include <queue>
#include <utility>
#include <vector>
#include <set>
#include <memory.h>
#include <iomanip>
#include <bitset>
#include <list>
#include <stack>
#include <deque>

using namespace std;

#define mod 1000000007

int n;
vector<vector<int> > child(1010);
vector<int> x(1010);
int dp[1010][5010];

int cansolve(int node)
{
	if(child[node].size() == 0) return 0;
	vector<pair<int, int> > tmpv;
	// cout << node << " : " << x[node] << endl;
	for(int i = 0; i < child[node].size(); i++){
		int childnode = child[node][i];
		int tmp = cansolve(childnode);
		if(tmp == mod) return mod;
		tmpv.push_back(make_pair(tmp, x[childnode]));
	}
	for(int i = 0; i < tmpv.size(); i++){
		for(int j = 0; j <= x[node]; j++){
			dp[i][j] = mod;
		}
	}
	if(tmpv[0].first <= x[node]) dp[0][tmpv[0].first] = tmpv[0].second;
	if(tmpv[0].second <= x[node]) dp[0][tmpv[0].second] = tmpv[0].first;
	for(int i = 1; i < tmpv.size(); i++){
		int fst = tmpv[i].first;
		int snd = tmpv[i].second;
		for(int j = fst; j <= x[node]; j++){
			dp[i][j] = min(dp[i][j], dp[i - 1][j - fst] + snd);
		}
		for(int j = snd; j <= x[node]; j++){
			dp[i][j] = min(dp[i][j], dp[i - 1][j - snd] + fst);
		}
	}
	int ans = mod;
	for(int i = 0; i <= x[node]; i++){
		ans = min(ans, dp[tmpv.size() - 1][i]);
	}
	// cout << node << " " << ans << " " << x[node] << endl;
	return ans;
}

int main()
{
	cin >> n;
	for(int i = 1; i < n; i++){
		int p;
		cin >> p;
		p--;
		child[p].push_back(i);
	}
	for(int i = 0; i < n; i++){
		cin >> x[i];
	}
	if(cansolve(0) != mod) cout << "POSSIBLE" << endl;
	else cout << "IMPOSSIBLE" << endl;
}