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 Main {
    static Scanner scn;

    ArrayList<Integer> g[];
    int a[];
    int s[];
    int p[];
    int n;

    void dfs(int v, int pref_sum) {
        // s[v] = -1
        if (g[v].size() == 0) {
            a[v] = 0;
            return;
        }

        int min_pref = (int)1e9;

        for (int u : g[v]) {
            min_pref = Math.min(min_pref, s[u]);
        }

        a[v] = min_pref - pref_sum;

        for (int u : g[v]) {
            a[u] = s[u] - a[v] - pref_sum;
        }

        for (int u : g[v]) {
            for (int w : g[u]) dfs(w, s[u]);
        }
    }

    public void go() {
        n = scn.nextInt();
        g = new ArrayList[n];
        s = new int[n];
        p = new int[n];
        a = new int[n];
        p[0] = -1;
        for (int i = 1; i < n; i++) {
            p[i] = scn.nextInt() - 1;
        }
        for (int i = 0; i < n; i++) {
            s[i] = scn.nextInt();
            g[i] = new ArrayList<>();
        }

        for (int i = 1; i < n; i++) {
            g[p[i]].add(i);
        }

        for (int u : g[0]) {
            dfs(u, s[0]);
        }

        a[0] = s[0];
        long ans = 0;
        for (int i = 0; i < n; i++) ans += a[i];
        for (int i = 0; i < n; i++) if (a[i] < 0) {
            System.out.println(-1);
            return;
        }
        System.out.println(ans);
    }

    public static void main(String args[]) {
        scn = new Scanner(System.in);
        new Main().go();
    }
}
