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.*;

public class Main {
    ArrayList<Integer>[] t;
    int[] s;
    int[] min;
    long ans;
    boolean error = true;
    public void solve() {
        int n = ni();
        t = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            t[i] = new ArrayList<>();
        }
        int[] ps = new int[n];
        for (int i = 1; i < n; i++) {
            int p = ni() - 1;
            t[p].add(i);
            ps[i] = p;
        }
        s = new int[n];
        min = new int[n];
        for (int i = 0; i < n; i++) {
            s[i] = ni();
            if (min[ps[i]] == 0) {
                min[ps[i]] = s[i];
            } else {
                min[ps[i]] = Math.min(s[i], min[ps[i]]);
            }
        }
        ans = s[0];
        error = false;
        dfs(0, -1);
        write((error ? -1 : ans) + "\n");
    }
    void dfs(int v, int p) {
        if (v != 0) {
            if (s[v] == -1) {
                s[v] = Math.max(min[v], s[p]);
            }
            if (s[v] < s[p]) {
                error = true;
                return;
            }
            ans += s[v] - s[p];
        }
        for (int ch: t[v]) {
            dfs(ch, v);
        }
    }






    public static void main(String[] args) {
        Main m = new Main();
        m.solve();
        try {
            m.out.close();
        } catch (IOException e) {}
    }

    BufferedReader in;
    BufferedWriter out;
    StringTokenizer tokenizer;
    public Main() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public String n() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(in.readLine());
            } catch (IOException e) {}
        }
        return tokenizer.nextToken();
    }
    public int ni() {
        return Integer.parseInt(n());
    }
    public void write(String s) {
        try {
            out.write(s);
        } catch (IOException e) {}
    }
}