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 sys
import io, os
import math
gcd=math.gcd
ceil=math.ceil
#arr=list(map(int, input().split()))
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
mod1=(10**9)+7
mod2=998244353
def strinp(testcases):
    k=5
    if(testcases==-1 or testcases==1):
        k=1
    f=str(input())
    f=f[2:len(f)-k]
    return f
def alp(a):
    return (ord(a)-ord("a"))
def main():
    n=int(input())
    graph=[[] for i in range(n)]
    par=list(map(int, input().split()))
    for i in range(n-1):
        graph[par[i]-1].append(i+1)
    arr=list(map(int, input().split()))
    ans=[-1]*n
    ans[0]=arr[0]
    stk=[]
    curr=0
    nvis = [True] * n
    level=[1]*n
    level[0]=[1,0]
    while(True):
        nxt = -1
        temp=len(graph[curr])
        for i in range(temp-1,-1,-1):
            if (nvis[graph[curr][i]]):
                nxt = graph[curr][i]
                break
            else:
                graph[curr].pop()
        if(stk!=[]):
            level[curr]=[level[stk[-1]][0]+1,curr]
        if(nxt != -1):
            stk.append(curr)
            nvis[curr] = False
            curr = nxt  
        else:
            if(curr==0):
                break
            nvis[curr] = False
            curr = stk[-1]
            stk.pop(-1)
    level.sort()
    graph=[[] for i in range(n)]
    for i in range(n-1):
        graph[par[i]-1].append(i+1)
    trig=False
    for i in range(n):
        if(level[i][0]%2==0):
            node=level[i][1]
            s1=arr[par[node-1]-1]
            temp=len(graph[node])
            if(temp==0):
                ans[node]=0
                continue
            mi=10**18
            for j in range(temp):
                s2=arr[graph[node][j]]
                if(s1>s2):
                    trig=True
                    break
                else:
                    mi=min(mi,s2-s1)
            if(trig):
                break
            ans[node]=mi
            for j in range(temp):
                s2=arr[graph[node][j]]
                ans[graph[node][j]]=s2-s1-ans[node]
    if(trig):
        print(-1)
    else:
        print(sum(ans))
if __name__ == '__main__':
    main()