#include <bits/stdc++.h>
using namespace std;
const int MAX = (5e3)+1, INF = 1e9;

int n, x[MAX], dp[MAX], f[2][MAX];
vector<int> g[MAX];

void dfs(int u) {
	for(int v: g[u]) dfs(v);
	fill(f[0], f[0]+MAX, INF);
	fill(f[1], f[1]+MAX, INF);
	f[0][0] = 0;
	int pre = 0, curr = 1;
	for(int v: g[u]) {
		for(int i = MAX - 1 - min(dp[v], x[v]); i >= 0; i--) {
			if(i + dp[v] < MAX) f[curr][i + dp[v]] = min(f[pre][i] + x[v], f[curr][i + dp[v]]);
			if(i + x[v] < MAX) f[curr][i + x[v]] = min(f[pre][i] + dp[v], f[curr][i + x[v]]);
		}
		fill(f[pre], f[pre]+MAX, INF);
		swap(pre, curr);
	}
	if(u == 1 || g[u].size()) for(int i = 0; i <= x[u]; i++) dp[u] = min(f[pre][i], dp[u]);
	else dp[u] = 0;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
	for(int i = 2, p; i <= n; i++) {
		cin >> p;
		g[p].push_back(i);
	}
	for(int i = 1; i <= n; i++) cin >> x[i];
	fill(dp+1, dp+n+1, INF);
	dfs(1);

	bool valid = true;
	for(int i = 1; i <= n; i++) valid &= dp[i] < INF;
	if(valid) cout << "POSSIBLE";
	else cout << "IMPOSSIBLE";
}

### Prompt

Please formulate a cpp solution to the following problem:

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`.

Examples

Input

3
1 1
4 3 2


Output

POSSIBLE


Input

3
1 2
1 2 3


Output

IMPOSSIBLE


Input

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3


Output

POSSIBLE


Input

1

0


Output

POSSIBLE

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAX = (5e3)+1, INF = 1e9;

int n, x[MAX], dp[MAX], f[2][MAX];
vector<int> g[MAX];

void dfs(int u) {
	for(int v: g[u]) dfs(v);
	fill(f[0], f[0]+MAX, INF);
	fill(f[1], f[1]+MAX, INF);
	f[0][0] = 0;
	int pre = 0, curr = 1;
	for(int v: g[u]) {
		for(int i = MAX - 1 - min(dp[v], x[v]); i >= 0; i--) {
			if(i + dp[v] < MAX) f[curr][i + dp[v]] = min(f[pre][i] + x[v], f[curr][i + dp[v]]);
			if(i + x[v] < MAX) f[curr][i + x[v]] = min(f[pre][i] + dp[v], f[curr][i + x[v]]);
		}
		fill(f[pre], f[pre]+MAX, INF);
		swap(pre, curr);
	}
	if(u == 1 || g[u].size()) for(int i = 0; i <= x[u]; i++) dp[u] = min(f[pre][i], dp[u]);
	else dp[u] = 0;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
	for(int i = 2, p; i <= n; i++) {
		cin >> p;
		g[p].push_back(i);
	}
	for(int i = 1; i <= n; i++) cin >> x[i];
	fill(dp+1, dp+n+1, INF);
	dfs(1);

	bool valid = true;
	for(int i = 1; i <= n; i++) valid &= dp[i] < INF;
	if(valid) cout << "POSSIBLE";
	else cout << "IMPOSSIBLE";
}

```