Mitya has a rooted tree with n vertices indexed from 1 to n, where the root has index 1. Each vertex v initially had an integer number a_v ≥ 0 written on it. For every vertex v Mitya has computed s_v: the sum of all values written on the vertices on the path from vertex v to the root, as well as h_v — the depth of vertex v, which denotes the number of vertices on the path from vertex v to the root. Clearly, s_1=a_1 and h_1=1.

Then Mitya erased all numbers a_v, and by accident he also erased all values s_v for vertices with even depth (vertices with even h_v). Your task is to restore the values a_v for every vertex, or determine that Mitya made a mistake. In case there are multiple ways to restore the values, you're required to find one which minimizes the total sum of values a_v for all vertices in the tree.

Input

The first line contains one integer n — the number of vertices in the tree (2 ≤ n ≤ 10^5). The following line contains integers p_2, p_3, ... p_n, where p_i stands for the parent of vertex with index i in the tree (1 ≤ p_i < i). The last line contains integer values s_1, s_2, ..., s_n (-1 ≤ s_v ≤ 10^9), where erased values are replaced by -1.

Output

Output one integer — the minimum total sum of all values a_v in the original tree, or -1 if such tree does not exist.

Examples

Input


5
1 1 1 1
1 -1 -1 -1 -1


Output


1


Input


5
1 2 3 1
1 -1 2 -1 -1


Output


2


Input


3
1 2
2 -1 1


Output


-1
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Scanner;

// keep all even level node as 0
public class D {
	public static void main(String[] args) throws Exception {
		solve();
	}

	// **SOLUTION**
	public static void solve() throws Exception {
		int n = sc.nextInt();
		int[] par = new int[n + 1];

		long[] s = new long[n + 1];
		long[] a = new long[n + 1];
		HashSet<Integer>[] c = new HashSet[n + 1];
		for (int i = 0; i <= n; i++)
			c[i] = new HashSet<>();

		par[1] = -1;
		for (int i = 2; i < par.length; i++) {
			par[i] = sc.nextInt();
			c[par[i]].add(i);
		}

		for (int i = 1; i <= n; i++)
			s[i] = sc.nextLong();

		boolean b = dfs(1, s, a, par, c, 1, 0);

		if (b) {
			long ans = 0;
			for (int i = 1; i <= n; i++)
				ans += a[i];
			System.out.println(ans);
		} else {
			System.out.println(-1);
		}
	}

	// h is of no use
	private static boolean dfs(int node, long[] s, long[] a, int[] par, HashSet<Integer>[] tree, int h, long sum) {
		if (h % 2 == 0) {
			if (tree[node].size() == 0) {
				a[node] = 0;
			} else {
				long min = Integer.MAX_VALUE;
				for (int child : tree[node])
					min = Math.min(min, s[child]);
				if (min < sum)
					return false;
				min -= sum;
				a[node] = min;
			}
			s[node] = sum + a[node];
		} else {
			if (sum > s[node])
				return false;
			a[node] = s[node] - sum;
		}
		for (int child : tree[node]) {
			boolean b = dfs(child, s, a, par, tree, h + 1, s[node]);
			if (!b)
				return false;
		}
		return true;
	}

	public static InputStreamReader r = new InputStreamReader(System.in);
	public static BufferedReader br = new BufferedReader(r);
	public static Scanner sc = new Scanner(System.in);
}
