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.ArrayList;
import java.util.Scanner;

public class que4 {

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			graph.add(new ArrayList<Integer>());
		}
		for (int i = 0; i < n - 1; i++) {
			int v = scn.nextInt();
			graph.get(v - 1).add(i + 1);
		}
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();
		}
		int[] ts = new int[n];
		boolean bs = dfs(0,-1, graph, 0, arr, ts);
		if (bs) {
			long sum = 0;
			for (int i = 0; i < ts.length; i++) {
				sum += ts[i];
			}
			System.out.println(sum);
		} else {
			System.out.println(-1);
		}

	}

	public static boolean dfs(int vertex, int par,ArrayList<ArrayList<Integer>> graph, int value, int[] arr, int[] ts) {
		if (arr[vertex] == -1) {
			int max=Integer.MAX_VALUE;
			for (int val : graph.get(vertex)) {
               max=Math.min(max, arr[val]);
			}
			if(max==Integer.MAX_VALUE){
				ts[vertex]=0;
			} else if(max<arr[par]){
				return false;
			}else{
			ts[vertex]=max-arr[par];}
			value=max;
			if(ts[vertex]<0){
				ts[vertex]=0;
			}
			
		} else {
			ts[vertex] = arr[vertex] - value;
			if (arr[vertex] < value) {
				boolean b = false;
				return false;
			}
		}
		for (int v : graph.get(vertex)) {
			if (arr[vertex] == -1) {
				boolean b = dfs(v,vertex, graph, value, arr, ts);
				if (!b) {
					return b;
				}
			} else {
				boolean s = dfs(v,vertex, graph, arr[vertex], arr, ts);
				if (!s) {
					return s;
				}
			}
		}
		return true;
	}

}
