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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class SumInTheTree {
    static int[] sv = new int[100000];
    static int[] av = new int[100000];
    static Vertex[] v = new Vertex[100000];
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(f.readLine());
        for (int i = 0; i < n; i++) {
            v[i] = new Vertex(i);
        }
        for (int i = 1; i < n; i++) {
            int a = Integer.parseInt(st.nextToken())-1;
            v[i].p = a;
            v[a].children.add(i);
        }
        st = new StringTokenizer(f.readLine());
        for (int i = 0; i < n; i++) {
            sv[i] = Integer.parseInt(st.nextToken());
        }
        av[0] = sv[0];
        dfs(0);
        PrintWriter out = new PrintWriter(System.out);
        long sum = 0;
        for (int i = 0; i < n; i++) {
            sum += av[i] * 1L;
        }
        out.println(sum);
        out.close();
    }
    static void dfs(int node) {
        if (av[node] == 0 && sv[node] == -1) {
            if (v[node].children.size() == 0) {
                av[node] = 0;
                return;
            }
            int minsv = Integer.MAX_VALUE;
            for (int c : v[node].children) {
                minsv = Math.min(sv[c] - sv[v[node].p], minsv);
            }
            if (minsv < 0) {
                System.out.println(-1);
                System.exit(0);
            }
            else {
                av[node] = minsv;
                sv[node] = sv[v[node].p] + minsv;
            }
        }
        else if (av[node] == 0) {
            av[node] = sv[node] - sv[v[node].p];
        }
        for (int c : v[node].children) {
            dfs(c);
        }
    }
    static class Vertex {
        ArrayList<Integer> children = new ArrayList<>();
        int id;
        int p;
        Vertex(int id) {
            this.id = id;
        }
    }
}
