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.*;
import java.io.*;
public class A {











    static boolean tests = false;
    static ArrayList<Integer> tree[];
    static long[] sum, node;
    static boolean flag;
    static void addEdge(int v, int u){
        if (tree[v] == null) tree[v] = new ArrayList<>();
        if (tree[u] == null) tree[u] = new ArrayList<>();
        tree[v].add(u);
        tree[u].add(v);
    }
    static void dfs(int v, int u, int d){
        if (d % 2 == 0){
            if (tree[v].size() == 1){
                node[v] = 0L;
                return;
            }
            // find min sum[child]-sum[u] in tree[v]
            long min = 2L*int_max;
            for (int to : tree[v]) if (to != u){
                min = Math.min(min, sum[to]-sum[u]);
            }
            node[v] = min;
            sum[v] = sum[u]+node[v];
        }else node[v] = sum[v]-sum[u];
        if (node[v] < 0){
            flag = false;
            return;
        }
        for (int to : tree[v]) if (to != u){
            dfs(to, v, d+1);
        }
    }
    static void solve(){
        int n = fs.nextInt();
        tree = new ArrayList[n+5];
        for (int i = 2; i <= n; ++i){
            int p = fs.nextInt();
            addEdge(p, i);
        }
        sum = new long[n+1];
        node = new long[n+1];
        sum[0] = 0L;
        for (int i = 1; i <= n; ++i){
            sum[i] =  fs.nextInt();
        }
        flag = true;
        dfs(1, 0, 1);
        if (!flag){
            out.println(-1);
            return;
        }
        long ans = 0L;
        for (long x : node) ans += x;
        out.println(ans);
    }















    static FastScanner fs;
    static PrintWriter out;
    static int int_max = (int)1e9, mod = int_max+7;
    public static void main(String[] args) {
        fs = new FastScanner();
        out = new PrintWriter(System.out);
        int t = 1;
        if (tests) t = fs.nextInt();
        while (t-- > 0) solve();
        out.close();
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readIntArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readLongArray(int n){
            long a[] = new long[n];
            for (int i = 0; i < n; ++i){
                a[i] = nextLong();
            }
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}