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>
using namespace std;
const int N = 2e5 + 50;
const int inf = 1e9 + 50;
const int mod = 1e9 + 7;
int read() {
  int k = 0, sig = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') sig *= -1;
    c = getchar();
  }
  while (isdigit(c)) {
    k = (k << 3) + (k << 1) + c - '0';
    c = getchar();
  }
  return k * sig;
}
int main() {
  vector<vector<int>> v(N);
  vector<int> siz(N, 0), st(N);
  int n = read();
  for (int i = 1; i <= n; i++) {
    int w = read();
    v[i].push_back(w);
  }
  int num = 0;
  for (int i = 1; i <= n; i++) num += read();
  int cnt = 1;
  std::function<void(int)> dfs = [&](int x) {
    siz[cnt]++;
    st[x] = cnt;
    for (auto y : v[x]) {
      if (st[y]) continue;
      dfs(y);
    }
  };
  bool ok = false, okk = false;
  int ans = 0;
  dfs(1);
  for (int i = 1; i <= n; i++) {
    if (st[i]) continue;
    ++cnt;
    dfs(i);
    okk = true;
    ans++;
  }
  printf("%d", ans + okk + (num % 2 ? 0 : 1));
}
