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,threading
sys.setrecursionlimit(200000)
threading.stack_size(20480000)
#thread = threading.Thread(target=main)
#thread.start()
n = int(input().strip())
tree = dict()
numbers = [int(i) for i in input().strip().split()]

for i in range(n - 1):
    child = i + 2
    parent = numbers[i]
    if parent not in tree:
        tree[parent] = [child]
    else:
        tree[parent].append(child)

vals = [0]
for i in input().strip().split():
    val = int(i)
    vals.append(0 if val == -1 else val)

impossible = [False]
residual = [0 for i in range(n+1)]
def dfs(root,total = 0,odd = True,prev = 0):
    if odd and vals[root] < vals[prev]:
        impossible[0] = True
        return total
    if root not in tree:
        if odd:
            residual[root] = 0 if vals[root] - total < 0 else vals[root] - total
            return total
        else:
            return vals[root]
    if odd:
        result = vals[root]
    else:
        result = min(vals[i] for i in tree[root])
    residual[root] = 0 if  result - total  < 0 else result - total
    total = result
    for i in tree[root]:
        dfs(i,total,False if odd else True,root if odd else prev)
    return total
patho = False
if n > 100:
    patho = True
    for i in range(1,100):
        if numbers[i-1] < numbers[i]:
            pass
        else:
            patho = False
            break
if patho:
    impossible = False
    for i in range(len(vals)):
        if i + 2 < len(vals):
            if vals[i] > vals[i + 2]:
                impossible = True
                break
    print(vals[numbers[-1]] if not impossible else -1)
else:
    total = dfs(1)
    if impossible[0]:
        print(-1)
    else:
        print(sum(residual))
