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
#!/usr/bin/env python
# coding: utf-8

# In[ ]:


n=int(input())
parents=['None']+list(map(int, input().rstrip().split()))
weights=list(map(int, input().rstrip().split()))


# In[102]:




# In[113]:


children = [[] for i in range(0,n)]


# In[104]:


#weightsum = dict(zip(seq, weights))


# In[114]:


weightvalue =[0]*n
weightvalue[0]=weights[0]


# In[115]:
#print(parents, children)


for i in range(1,n):
    k=parents[i]
    children[k-1].append(i+1)
    


# In[116]:




# In[119]:


check=0


for i in range(1,n):
    if weights[i]==-1:
        if not children[i]==[]:
            childweights=[]
            for c in children[i]:
                childweights.append(weights[c-1])
            m=min(childweights)
        else:
            m=weights[parents[i]-1]
        if m<weights[parents[i]-1]:     
            check=-1
        else:
            weightvalue[i]=m-weights[parents[i]-1]
            weights[i]=weights[parents[i]-1]+weightvalue[i]
        #print(m,weights[i], weightvalue[i])    
            
    else:
        
        if weights[i]-weights[parents[i]-1]<0:
            check=-1
        else:
            weightvalue[i]=weights[i]-weights[parents[i]-1]
    
#print(weights, weightvalue)    
            
            
if check==-1:
    print(-1)
    
else:
    print(sum(weightvalue))


# In[ ]:

