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.
#include <bits/stdc++.h>
namespace std {
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_set = std::unordered_set<_Key, _Hash>;
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_mset = std::unordered_multiset<_Key, _Hash>;
template <typename _Key, typename _Val, typename _Hash = std::hash<_Key>>
using hash_map = std::unordered_map<_Key, _Val, _Hash>;
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_mmap = std::unordered_multimap<_Key, _Hash>;
template <typename _Key, typename _Cmp = std::less<_Key>>
using mset = std::multiset<_Key, _Cmp>;
template <typename _Key, typename _Val, typename _Cmp = std::less<_Key>>
using mmap = std::multimap<_Key, _Val, _Cmp>;
template <typename _Key>
using rset = std::set<_Key, std::greater<_Key>>;
template <typename _Key>
using rmset = std::multiset<_Key, std::greater<_Key>>;
template <typename _Key, typename _Val>
using rmap = std::map<_Key, std::greater<_Key>>;
template <typename _Key, typename _Val>
using rmmap = std::multimap<_Key, _Val, std::greater<_Key>>;
static std::ostream& fdeb = cerr;
struct NullOstream {};
template <typename T>
NullOstream& operator<<(NullOstream& out, const T&) {
  return out;
}
NullOstream& operator<<(NullOstream& out, std::ostream& (*)(std::ostream&)) {
  return out;
}
static NullOstream deb;
static NullOstream debl;
template <int _Ind, typename... _Args>
struct __TuplePrinter {
  static void print(ostream& out, const tuple<_Args...>& t) {
    __TuplePrinter<_Ind - 1, _Args...>::print(out, t);
    out << ' ' << get<_Ind>(t);
  }
};
template <typename... _Args>
struct __TuplePrinter<0, _Args...> {
  static void print(ostream& out, const tuple<_Args...>& t) {
    out << '(' << get<0>(t);
  }
};
template <typename... _Args>
ostream& operator<<(ostream& out, const tuple<_Args...>& t) {
  __TuplePrinter<sizeof...(_Args) - 1, _Args...>::print(out, t);
  out << ')';
  return out;
}
template <typename _T1, typename _T2>
ostream& operator<<(ostream& out, const pair<_T1, _T2>& p) {
  return out << '(' << p.first << ' ' << p.second << ')';
}
using uchar = unsigned char;
using ushort = unsigned short;
using uint = unsigned int;
using lld = long long;
using ulld = unsigned long long;
static const int MOD = 1e9 + 7;
static const int INF = MOD;
static const lld HASHP = 37;
}  // namespace std
using namespace std;
void num_ones(std::vector<int>& p, int ind) {
  int len = 0;
  while (p[ind] >= 0) {
    ++len;
    auto ind_ = ind;
    ind = p[ind];
    p[ind_] = -1;
    deb << ind;
  }
  debl << ';';
}
int main() {
  std::ios::sync_with_stdio(false);
  int n;
  std::cin >> n;
  std::vector<int> p(n);
  for (auto& v : p) {
    std::cin >> v;
    --v;
  }
  int num1 = 0;
  for (int i = 0; i < n; ++i) {
    int v;
    std::cin >> v;
    num1 += !!v;
  }
  int num_cyc = 0;
  for (int i = 0; i < n; ++i) {
    if (p[i] == -1) continue;
    num_ones(p, i);
    ++num_cyc;
  }
  debl << "nc" << num_cyc;
  num1 = (num1 + 1) % 2;
  int result = (num_cyc == 1 ? 0 : num_cyc);
  std::cout << (result + num1) << std::endl;
  return 0;
}
