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 Codechef {
    static final long[] p = new long[200005], s = new long[200005], a = new long[200005];
    static final long[] newSum = new long[200005];
    static ArrayList<Long>[] g = new ArrayList[200005];
    static boolean[] visited = new boolean[200005];
    static boolean mistake  = false;

    public static void dfs(long u, long h, long sum) {
        long foo = s[(int)u];
        if(h%2 == 1) {
            if(sum > foo || foo<0) {
                mistake = true;
                return;
            }
            sum = foo;
        } else {
            if(foo>=0) {
                mistake = true;
                return;
            }
        }
        for(long x: g[(int)u]) {
            dfs(x, h+1, sum);
        }
    }

    public static void dfsFill(long u, long h, long sum) {
        if(h%2 == 0) {
            long mnVal = 2000000000L;
            boolean child = false;

            for(long x: g[(int)u]) {
                mnVal = Math.min(mnVal, s[(int)x]);
                child = true;
            }

            if(child == false) {
                mnVal = newSum[(int)p[(int)u]];
            }

            long thisVal = mnVal - newSum[(int)p[(int)u]];
            a[(int)u] = thisVal;
            newSum[(int)u] = mnVal;
        } else {
            if(u==1) {
                newSum[1] = a[1] = s[1];
            } else {
                a[(int)u] = s[(int)u] - newSum[(int)p[(int)u]];
                newSum[(int)u] = s[(int)u];
            }
        }
        for(long x: g[(int)u]) {
            dfsFill(x, h+1, newSum[(int)u]);
        }
    }

    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        long n = scanner.nextInt();

        for(int i = 1; i<=n; i++) {
            g[i] = new ArrayList<>();
            visited[i] = false;
        }

        for(int i = 2; i<=n; i++) {
            p[i] = scanner.nextLong();
            g[(int)p[i]].add((long)i);
        }

        for(int i = 1; i<=n; i++) {
            s[i] = scanner.nextLong();
        }

        dfs(1, 1, 0);

        if(mistake == true) {
            System.out.println(-1);
            return;
        }

        dfsFill(1, 1, 0);
        long ans = 0;
        for(int i=1; i<=n; i++) {
            //System.out.println(a[i]);
            ans += a[i];
        }
        System.out.println(ans);
    }
}
