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.*;
import java.lang.*;
import java.math.*;

public class D_1099 implements Runnable{
    List<Integer> list[];
    public void solve(){
        int n = scan.nextInt();
        int ar[] = new int[n];
        list = new List[n];
        for(int i=0;i<n;i++){
            list[i] = new ArrayList<>();
        }
        for(int i=1;i<n;i++){
            int x = scan.nextInt()-1;
            list[i].add(x);
            list[x].add(i);
        }
        sv = new int[n];
        d = new int[n];
        a = new int[n];
        for(int i=0;i<n;i++) sv[i]= scan.nextInt();
        d[0] = 1;
        a[0] = sv[0];
        dfs1(0,-1);
        dfs2(0,-1);
        long sum = 0;
        for(int i=0;i<n;i++){
            if(a[i]<0){
                out.println("-1");
                return;
            }
            sum+=a[i];
        }
        out.println(sum);
    }
    int sv[],d[],a[];
    void dfs1(int src,int par){
        int min = Integer.MAX_VALUE;
        for(int i: list[src]){
            if(i==par) continue;
            d[i] = 1+d[src];
            dfs1(i,src);
            if(d[src]%2==0){
                min = Math.min(min,sv[i]);
            }
        }
        if(sv[src]==-1){
            sv[src] = (min==Integer.MAX_VALUE)?sv[par]:min;
        }
        return;
    }
    
    void dfs2(int src,int par){
        for(int i : list[src]){
            if(i==par){
                continue;
            }
            a[i] = sv[i]-sv[src];
            dfs2(i,src);
        }
    }

    InputReader scan;
    PrintWriter out;
    
    @Override
    public void run(){
        scan = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();
    }
    
    public static void main(String[] args) {
        new Thread(null,new D_1099(),"Main",1<<26).start();
    }
    
    
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        
        public int read() {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
        
        public long[] nla(int n){ //nextLongArray()
            long ar[] = new long[n];
            for(int i=0;i<n;i++){
                ar[i] = this.nextLong();
            }
            return ar;
        }

        public int[] nia(int n){
            int ar[] = new int[n];
            for(int i=0;i<n;i++){
                ar[i] = this.nextInt();
            }
            return ar;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

}