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.util.*;

public class TreeSum {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int num = Integer.parseInt(scan.nextLine());
		int[] parents = new int[num - 1];
		StringTokenizer str = new StringTokenizer(scan.nextLine());
		for (int i = 0; i < num - 1; i++) {
			parents[i] = Integer.parseInt(str.nextToken());
		}
		int sums[] = new int[num];
		str = new StringTokenizer(scan.nextLine());
		for (int i = 0; i < num; i++) {
			sums[i] = Integer.parseInt(str.nextToken());
		}
		Node[] nodes = new Node[num];
		nodes[0] = new Node(1, sums[0], sums[0], 1, null);
		for (int i = 1; i < nodes.length; i++) {
			nodes[i] = new Node(i + 1, -1, sums[i], nodes[parents[i - 1] - 1].depth + 1, nodes[parents[i - 1] - 1]);
			nodes[parents[i - 1] - 1].addChild(nodes[i]);
		}
		dfs(nodes[0]);
		long sum = dfsSum(nodes[0]);

		if (sum <= -1) {
			System.out.println(-1);
		} else {
			System.out.println(sum + nodes[0].val);
		}
	}

	public static void dfs(Node root) {
		// int sum = 0;
		if (root.sum == -1) {
			if (root.children.size() > 0) {
				int min = Integer.MAX_VALUE;
				for (Node s : root.children) {
					min = Math.min(min, s.sum);
				}
				// System.out.println(min);
				if (min < root.parent.sum) {
					root.val = -10;
					return;
				} else {
					root.sum = min;
					root.val = root.sum - root.parent.sum;
				}
			} else {
				root.val = 0;
				root.sum = root.parent.sum;
			}
		} else {
			if (root.parent != null) {
				root.val = root.sum - root.parent.sum;
			}
		}
		if (root.children.size() > 0) {
			for (Node n : root.children) {
				dfs(n);
			}
		}
	}

	public static long dfsSum(Node root) {
		long sum = 0;
		if (root.children.size() > 0) {
			for (int i = 0; i < root.children.size(); i++) {
				// System.out.println(root.children.get(i).val + ", " +
				// root.children.get(i).index);
				if (root.children.get(i).val != -10) {
					sum += root.children.get(i).val;
				} else {
					sum = -1000000000;
					// System.out.println(sum);
				}
				sum += dfsSum(root.children.get(i));
			}
		}
		return sum;
	}
}

class Node {
	public int index;
	public int val;
	public int sum;
	public int depth;

	public Node parent;

	public ArrayList<Node> children;

	public Node(int i, int v, int s, int d, Node p) {
		index = i;
		val = v;
		sum = s;
		depth = d;
		parent = p;
		children = new ArrayList<Node>();
	}

	public void addChild(Node obj) {
		children.add(obj);
	}
}