#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<double> CMP;

class TurnOnLamps { public:
	typedef int Vert;
	struct Edge {
		bool init;
		bool goal;
		Vert from;
		Vert to;
	};

	int minimize(vector <int> roads, string initState, string isImportant)
	{
		int N = roads.size() + 1;
		vector< vector<Edge> > G(N);
		for(int i=0; i<roads.size(); ++i)
		{
			int v = i+1;
			int u = roads[i];
			{Edge e = {initState[i]=='1', isImportant[i]=='1', v, u}; G[v].push_back(e);}
			{Edge e = {initState[i]=='1', isImportant[i]=='1', u, v}; G[u].push_back(e);}
		}

		Edge e = {false, false, -1, 0};
		pair<int,int> rr = rec(e, G);
		return min(rr.first, rr.second);
	}

	static const int INF = 999999;

	// not use, use
	pair<int,int> rec(Edge e, vector<vector<Edge> >& G)
	{
		vector< pair<int,int> > p;
		for(int i=0; i<G[e.to].size(); ++i)
		{
			Edge& e2 = G[e.to][i];
			if(e2.to != e.from)
				p.push_back(rec(e2, G));
		}
		pair<int,int> r = calc_on_node(p);
		if(e.goal)
			(e.init ? r.second : r.first) = INF;
		return r;
	}

	pair<int,int> calc_on_node(vector<pair<int,int> >& c)
	{
		int nu = calc(c);
		int u = (c.empty() ? 1 : INF);
		for(int i=0; i<c.size(); ++i)
		{
			vector<pair<int,int> > cc = c;
			cc.erase(cc.begin() + i);
			int s1 = calc(cc);
			int s2 = min(c[i].first + 1, c[i].second);
			u = min(u, s1+s2);
		}
		return make_pair(nu, u);
	}

	int calc(vector<pair<int,int> >& c)
	{
		int od = INF;
		int ev = 0;
		for(int i=0; i<c.size(); ++i)
		{
			int c0 = c[i].first;
			int c1 = c[i].second;

			int od2 = min(ev+c1, od+c0);
			int ev2 = min(ev+c0, od+c1-1);
			od = od2, ev = ev2;
		}
		return min(od, ev);
	}
};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
 bool ok = (Expected == Received);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, TurnOnLamps().minimize(roads, initState, isImportant));}
int main(){

CASE(0)
	int roads_[] = {0,0,1,1};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "0001"; 
	string isImportant = "0111"; 
	int _ = 1; 
END
CASE(1)
	int roads_[] = {0,0,1,1};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "0000"; 
	string isImportant = "0111"; 
	int _ = 2; 
END
CASE(2)
	int roads_[] = {0,0,1,1,4,4};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "000100"; 
	string isImportant = "111111"; 
	int _ = 2; 
END
CASE(3)
	int roads_[] = {0,0,1,1,4,4};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "100100"; 
	string isImportant = "011101"; 
	int _ = 2; 
END
CASE(4)
	int roads_[] = {0,0,2,2,3,1,6,3,1};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "010001110"; 
	string isImportant = "000110100"; 
	int _ = 1; 
END
CASE(5)
	int roads_[] = {0,0,1,2,4,4,6,1,2,5,2,8,8,3,6,4,14,7,18,14,11,7,1,12,7,5,18,23,0,14,11,10,2,2,6,1,30,11,9,12,5,35,25,11,23,17,14,45,15};
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = "0000000000010000000000000010000010100000000000000"; 
	string isImportant = "1010111111111011011111000110111111111111111110111"; 
	int _ = 14; 
END
/*
CASE(6)
	int roads_[] = ;
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = ; 
	string isImportant = ; 
	int _ = ; 
END
CASE(7)
	int roads_[] = ;
	  vector <int> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_)); 
	string initState = ; 
	string isImportant = ; 
	int _ = ; 
END
*/
}
// END CUT HERE
