Pavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction.

Pavel has a plan: a permutation p and a sequence b1, b2, ..., bn, consisting of zeros and ones. Each second Pavel move skewer on position i to position pi, and if bi equals 1 then he reverses it. So he hope that every skewer will visit every position in both directions.

Unfortunately, not every pair of permutation p and sequence b suits Pavel. What is the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements? Note that after changing the permutation should remain a permutation as well.

There is no problem for Pavel, if some skewer visits some of the placements several times before he ends to cook. In other words, a permutation p and a sequence b suit him if there is an integer k (k ≥ 2n), so that after k seconds each skewer visits each of the 2n placements.

It can be shown that some suitable pair of permutation p and sequence b exists for any n.

Input

The first line contain the integer n (1 ≤ n ≤ 2·105) — the number of skewers.

The second line contains a sequence of integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the permutation, according to which Pavel wants to move the skewers.

The third line contains a sequence b1, b2, ..., bn consisting of zeros and ones, according to which Pavel wants to reverse the skewers.

Output

Print single integer — the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements.

Examples

Input

4
4 3 2 1
0 1 1 1


Output

2


Input

3
2 3 1
0 0 0


Output

1

Note

In the first example Pavel can change the permutation to 4, 3, 1, 2.

In the second example Pavel can change any element of b to 1.
import sys
sys.setrecursionlimit(10000000)
import itertools
from fractions import gcd
from math import sqrt
from bisect import bisect_left
import heapq
from collections import deque
import sys
#codechef sucks!
#codeforces sucks sucks!
#me sucks sucks sucks
def Ls():
	return list(raw_input())
def get(a):
	return map(a ,raw_input().split())
def Int():
	return int(raw_input())
def Str():
	return raw_input()

def cc(vertices, edges):
        def find(x):
            if parent[x] != x:
                parent[x] = find(parent[x])
            return parent[x]
            
        def union(xy):
            x, y = map(find, xy)
            if rank[x] < rank[y]:
                parent[x] = y
            else:
                parent[y] = x
                if rank[x] == rank[y]:
                    rank[x] += 1
        
        parent, rank = {i:i for i in vertices}, {i:0 for i in vertices}
        map(union, edges)
        return len({find(x) for x in parent})
n = input()
h1 = get(int)
v1 = get(int)
edg = []
vert = range(1,n+1)
graph = {i:[] for i in vert}
for i in xrange(n):
	to = h1[i]
	edg.append((i+1,to))

cyl = cc(vert , edg)
#print cyl
ans = (0 if cyl == 1 else cyl)
if sum(v1) % 2 == 0:
	ans += 1
print ans





