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.IOException;
import java.util.*;
public class d {
    public static void main(String[] args) throws IOException {
        Scanner s = new Scanner(System.in);
    //BufferedReader s=new BufferedReader(new InputStreamReader(System.in));
        //       String[] st=s.readLine().trim().split("\\s+");
        //      a=Integer.parseInt(st[i]);
        //  String[] st1=s.readLine().trim().split("\\s+");
        StringBuilder sb = new StringBuilder();
        StringBuilder sb1 = new StringBuilder();
      int n=s.nextInt();
      ArrayList<Integer> [] adj=new ArrayList[n+1];
      for(int i=2;i<=n;i++){
          int par=s.nextInt();
          if(adj[par]==null) adj[par]=new ArrayList<>();
          adj[par].add(i);
      }
      long[] sum=new long[n+1];vis=new int[n+1];ans=new long[n+1];
      for(int i=1;i<=n;i++) {
          sum[i]=s.nextInt();
      }flag=0;long fu=0;
      dfs(0,1,sum,adj);
      if(flag==1) System.out.println(-1);
      else{
          for(int i=1;i<=n;i++) fu+=ans[i];
          System.out.println(fu);
      }
    }
    static int[] vis;static long[] ans;static int flag;
    public static int countSetBits(int n)
    {
        return (BitsSetTable256[n & 0xff]
                + BitsSetTable256[(n >> 8) & 0xff]
                + BitsSetTable256[(n >> 16) & 0xff]
                + BitsSetTable256[n >> 24]);
    }
    static int[] BitsSetTable256 ;
    public static void initialize(int n)
    {
        BitsSetTable256[0] = 0;
        for (int i = 0; i <=Math.pow(2,n); i++) {
            BitsSetTable256[i] = (i & 1) + BitsSetTable256[i / 2];
        }
    }
    static HashMap<Integer,Integer>[] val;//static int[] vis;static int y;
    static void dfs(long presum,int i ,long[] sum,ArrayList<Integer>[] adj){
      vis[i]=1;
       if(sum[i]==-1) ans[i]=0;
       else{
           if(presum>sum[i]){
               flag=1;return;
           }
           ans[i]=sum[i]-presum;
       }
       if(adj[i]==null) return;
       long min=Integer.MAX_VALUE;
       for(int j:adj[i]){
           if(vis[j]==0){
               min=Math.min(min,sum[j]);
           }
       }
       if(min!=-1&&min<presum){
           flag=1;return;
       }
       for(int j:adj[i]){
           if(vis[j]==0){
               if(sum[i]!=-1) dfs(sum[i],j,sum,adj);
               else {ans[i]=min-presum;dfs(min,j,sum,adj);}
           }
       }

    }

    static  void computeLPSArray(String pat, int M, int lps[]) {
        int len = 0;
        int i = 1;
        lps[0] = 0;
        while (i < M) {
            if (pat.charAt(i) == pat.charAt(len)) {
                len++;
                lps[i] = len;
                i++;
            }
            else
            {
                if (len != 0) {
                    len = lps[len - 1];
                }
                else
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }
    static boolean isPrime(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;

        if (n % 2 == 0 || n % 3 == 0) return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }
    static long powerwithmod(long  x, long y, int p) {
        long  res = 1;
        x = x % p;
        while (y > 0) {
            if ((y & 1) == 1)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }
    static long  powerwithoutmod(long x, int y) {
        long  temp;
        if( y == 0)
            return 1;
        temp = powerwithoutmod(x, y/2);
        if (y%2 == 0)
            return temp*temp;
        else
        {
            if(y > 0)
                return x * temp * temp;
            else
                return (temp * temp) / x;
        }
    }
    static void fracion(double x) {
        String a = "" + x;
        String spilts[] = a.split("\\."); // split using decimal
        int b = spilts[1].length(); // find the decimal length
        int denominator = (int) Math.pow(10, b); // calculate the denominator
        int numerator = (int) (x * denominator); // calculate the nerumrator Ex
        // 1.2*10 = 12
        int gcd = (int) gcd((long) numerator, denominator); // Find the greatest common
        // divisor bw them
        String fraction = "" + numerator / gcd + "/" + denominator / gcd;
        // System.out.println((denominator/gcd));
        long x1 = modInverse(denominator / gcd, 998244353);
        //  System.out.println(x1);
        System.out.println((((numerator / gcd) % 998244353 * (x1 % 998244353)) % 998244353));
    }
    static int bfs(int i1, ArrayList<Integer>[] h, int[] vis, int n,int val1) {
        Queue<Integer> q = new LinkedList<Integer>();
        q.add(i1);Queue<Integer> aq=new LinkedList<Integer>();
        aq.add(0);
        while(!q.isEmpty()){
            int i=q.poll();
            int val=aq.poll();
            if(i==n){
                return val;
            }
            if(h[i]!=null){
                for(Integer j:h[i]){
                    if(vis[j]==0){
                        q.add(j);vis[j]=1;
                        aq.add(val+1);}
                }
            }
        }return -1;
    }
    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static long modInverse(long a, int m)
    {
        return (powerwithmod(a, m - 2, m));
    }
    static int MAXN;
    static int[] spf=new int[MAXN];
    static void sieve() {
        spf[1] = 1;
        for (int i=2; i<MAXN; i++)
            spf[i] = i;
        for (int i=4; i<MAXN; i+=2)
            spf[i] = 2;
        for (int i=3; i*i<MAXN; i++)
        {
            if (spf[i] == i)
            {
                for (int j=i*i; j<MAXN; j+=i)

                    if (spf[j]==j)
                        spf[j] = i;
            }
        }
    }
    static ArrayList<Integer> getFactorizationUsingSeive(int x) {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        while (x != 1)
        {
            ret.add(spf[x]);
            x = x / spf[x];
        }
        return ret;
    }
   static long[] fac ;
     static void calculatefac(int mod){
         fac[0]=1;
        for (int i = 1 ;i <= MAXN; i++)
            fac[i] = fac[i-1] * i % mod;
     }
      static long nCrModPFermat(int n, int r, int mod) {
         if (r == 0)
            return 1;
        fac[0] = 1;
        return (fac[n]* modInverse(fac[r], mod)
                % mod * modInverse(fac[n-r], mod)
                                    % mod) % mod;
    } }
class Student {
    long  l;long r;int x;
    public Student(long l, long r) {
        this.l = l;
        this.r = r;this.x=x;
    }

    public String toString()
    {
        return this.l+" ";
    }
}
class Sortbyroll implements Comparator<Student>
{

    public int compare(Student a, Student b){
      if(a.l<b.l) return 1;
      else if(a.l==b.l){
          if(a.r==b.r){
              return 0;
          }
          if(a.r<b.r) return -1;
          return 1;}
      return -1;  }
}