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, os
input = sys.stdin.readline
read = lambda: list(map(int, input().strip().split()))

def main():
	n = int(input()); 
	par = [0, 0]+read(); 
	sm = [0]+read()
	child = [[] for i in range(n+1)]

	for i in range(2, n+1):
		child[par[i]].append(i)

	stk = [(1,1)]
	ans = 0

	while stk:
		node, f = stk.pop()
		
		if not f:
			if not child[node]:
				mn = sm[par[node]]
			else:
				mn = 10**9
				for x in child[node]:
					mn = min(mn, sm[x])
					stk.append((x, 1))

			if mn < sm[par[node]]:print(-1);exit()
			sm[node] = mn
			ans += mn - sm[par[node]]

		else:
			ans += sm[node] - sm[par[node]]

			for x in child[node]:
				stk.append((x, 0))
	print(ans)

if __name__ == "__main__":
	main()