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
def f(n, father, summ):
    tree_figlio = {}
    tree_papa = {}
    a = {}
    for i in range(0,n):
        tree_papa[i] = []
        a[i] = -1
    for i in range(0,n-1):
        tree_figlio[i+1] = father[i]-1
        tree_papa[father[i]-1].append(i+1)
    a[0] = summ[0]
    for i in range(1, n):
        if summ[i] == -1:
            if tree_papa[i] == []:
                a[i] = 0
            else:
                minimo = 1e10
                for j in tree_papa[i]:
                    minimo = min(minimo, summ[j])
                a[i] = minimo - summ[tree_figlio[i]]
            summ[i] = a[i] + summ[tree_figlio[i]]
        else:
            a[i] = summ[i] - summ[tree_figlio[i]]
    summa = 0
    for i in range(n):
        if a[i] < 0:
            return -1
        else:
            summa += a[i]
    return summa
    
if __name__ == '__main__':
    n = int(input())
    father = map(int, raw_input().rstrip().split())
    summ = map(int, raw_input().rstrip().split())
    print f(n, father, summ)