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.*;
import java.util.ArrayList;
import java.util.List;

/**
 * Created by vaibhav on 5/1/19.
 */
public class CF {

    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static OutputStream out = new BufferedOutputStream( System.out );
    public static boolean possible = true;
    public static  List<Integer>[] adjList;
    public static int[] s;
    public static int[] a;
    public static void main(String[] args) throws IOException {
        int n = readInt();
        int[] p = readIntArray();
        s = readIntArray();
        int[] newS = new int[n+1];
        for (int i = 1; i < n + 1; i++) {
            newS[i] = s[i-1];
        }
        s = newS;
        adjList = new List[n+1];
        for (int i = 0; i <= n; i++) {
            adjList[i] = new ArrayList<>();
        }
        for (int i = 0; i < n - 1; i++) {
            adjList[p[i]].add(i+2);
        }
        a = new int[n+1];
        for (int i = 0; i <= n; i++) {
            a[i] = -1;
        }
        a[1] = s[1];
        dfs(1,1,a[1]);
        long sum = 0;
        for (int i = 1; i < n+1; i++) {
            sum += a[i];
            if(a[i]<0) {
                possible = false;
                break;
            }
        }
        if(possible) {
            System.out.println(sum);
        }
        else {
            System.out.println(-1);
        }
    }

    private static void dfs(int node, int h, int sum) {
        if(h%2==1) {
            for (int i = 0; i < adjList[node].size(); i++) {
                dfs(adjList[node].get(i), h+1, s[node]);
            }
        }
        else {
            int mini = Integer.MAX_VALUE;
            for (int i = 0; i < adjList[node].size(); i++) {
                mini = Math.min(mini, s[adjList[node].get(i)]);
            }
            if(mini!=Integer.MAX_VALUE) {
                a[node] = mini - sum;
                s[node] = mini;
                for (int i = 0; i < adjList[node].size(); i++) {
                    a[adjList[node].get(i)] = s[adjList[node].get(i)] - s[node];
                }
                for (int i = 0; i < adjList[node].size(); i++) {
                    dfs(adjList[node].get(i), h+1, s[node]);
                }
            }
            else {
                a[node] = 0;
                s[node] = sum + a[node];
            }
        }
    }

    private static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    private static int[] readIntArray() throws IOException {
        String[] inp = br.readLine().split(" ");
        int[] o = new int[inp.length];
        for (int i = 0; i < inp.length; i++) {
            o[i] = Integer.parseInt(inp[i]);
        }
        return o;
    }

    private static long[] readLongArray() throws IOException {
        String[] inp = br.readLine().split(" ");
        long[] o = new long[inp.length];
        for (int i = 0; i < inp.length; i++) {
            o[i] = Long.parseLong(inp[i]);
        }
        return o;
    }

}
