1098_A. Sum in the tree
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
```python
# alpha = "abcdefghijklmnopqrstuvwxyz"
prime = 998244353 
# INF = 100000000000
# from heapq import heappush
from collections import defaultdict, deque
t = 1#int(input())
from math import sqrt
for test in range(t):
    n = int(input())
    p = [0, 0]
    p.extend(list(map(int, input().split())))
    s = [0]
    s.extend(list(map(int, input().split())))
    a = [0 for i in range(n+1)]
    a[1] = s[1]
    D = defaultdict(list)
    depth = {}
    depth[1] = 1
    # S[1] = 
    for i in range(2,n+1):
        D[p[i]].append(i)
        depth[i] = depth[p[i]]+1
    q = deque([])
    q.append(1)

    found = True
    while q:
        cur = q.popleft()
        if not found:
            break
        for j in D[cur]:
            if depth[j]%2==0:
                if D[j]==[]:
                    a[j] = 0
                    s[j] = s[cur]
                else:
                    tmp = 2000000000
                    for k in D[j]:                   
                        tmp = min(tmp, s[k] - s[cur])
                    if tmp<0:
                        found = False
                        break
                    a[j] = tmp
                    s[j] = s[cur]+tmp
                    for k in D[j]:                   
                        a[k] = s[k]-tmp-s[cur]

            else:
                if a[k]<0:
                    # print(k,a[k])
                    found = False
                    break
            q.append(j)
    if found:
        print(sum(a))
    else:
        print(-1)




    


        



```