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 <vector>
using namespace std;
const int MAXN = 1005;
const int inf = 1e9;
vector<int> adj[MAXN];
int n, x[MAXN];
int f[MAXN][2];
int g[MAXN][MAXN * 5];
void dfs(int u) {
    for(int i = 0; i < adj[u].size(); i++) dfs(adj[u][i]);
    for(int k = 0; k < 2; k++) {
        for(int i = 1; i <= adj[u].size(); i++) {
            int v = adj[u][i - 1];
            for(int j = 0; j <= x[u]; j++) {
                g[i][j] = inf;
                if(x[v] <= j) g[i][j] = std::min(g[i][j], g[i - 1][j - x[v]] + f[v][k]);
                if(f[v][k ^ 1] <= j) g[i][j] = std::min(g[i][j], g[i - 1][j - f[v][k ^ 1]] + x[v]);
            }
        }
        f[u][k] = g[adj[u].size()][x[u]];
    }
}
int main() {
    scanf("%d", &n);
    for(int i = 2; i <= n; i++) {
        int p; scanf("%d", &p);
        adj[p].push_back(i);
    }
    for(int i = 1; i <= n; i++) scanf("%d", &x[i]);
    dfs(1);
    if(f[1][0] < inf || f[1][1] < inf) printf("POSSIBLE\n");
    else printf("IMPOSSIBLE\n");
    return 0;
}