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
//package codeforces;

import java.util.ArrayList;
import java.util.Scanner;

public class SumTree {
	
	public static class TreeNode{
		long val;
		ArrayList<TreeNode> children;
		TreeNode(long val){
			this.val = val;
			this.children = new ArrayList<>();
		}
	}
	private static int set = 0;
	public static void calcSumDFS(TreeNode root,boolean isEven,long prevVal) {
		if(!isEven) {
			for(TreeNode n : root.children) {
				calcSumDFS(n,!isEven,root.val);
			}
		}else {
			long minVal = Integer.MAX_VALUE;
			for(TreeNode n : root.children) {
				if(minVal > n.val)
					minVal = n.val;
			}
			if((minVal - prevVal) < 0) {
				if(set == 0)
					set = 1;
				return;
			}
			if(root.children.size() != 0)
				root.val = minVal - prevVal;
			else
				root.val = 0;
			for(TreeNode n : root.children) {
				calcSumDFS(n,!isEven,root.val);
				n.val -= (prevVal + root.val);
			}
		}
	}
	
	private static long sumAll(TreeNode node) {
		if(node == null) return 0;
		long tot = node.val;
		for(TreeNode n : node.children)
			tot += sumAll(n);
		return tot;
	}
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		TreeNode[] nodes = new TreeNode[n];
		for(int i=0;i<nodes.length;i++)
			nodes[i] = new TreeNode(-1);
		for(int i=0;i<n-1;i++) {
			int pIdx = in.nextInt() - 1;
			nodes[pIdx].children.add(nodes[i+1]);
		}
		for(int i=0;i<n;i++) {
			nodes[i].val = in.nextLong();
		}
		calcSumDFS(nodes[0],false,-2);
		if(set == 1)
			System.out.println("-1");
		else
			System.out.println(sumAll(nodes[0]));
		in.close();
	}
}
