#include<bits/stdc++.h>
#define int long long
#define rep(i,a,b) for(int i(a);i<=(b);++i)
#define req(i,a,b) for(int i(a);i>=(b);--i)
#define sort stable_sort
using namespace std;
char buf[1<<23],*p1=buf,*p2=buf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
template<typename TP> inline TP read(TP &num)
{
	TP x=0;
	int f=0;
	char ch=getchar();
	while(ch<48||ch>57) f|=ch=='-',ch=getchar();
	while(48<=ch&&ch<=57) x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
	return num=f?-x:x;
}
template<typename ...Args> inline void read(Args &...args)
{
	(read(args),...);
}
template<typename TP> inline void write(TP x)
{
	(x<0)?(putchar('-'),x=-x):0;
	(x>9)?(write(x/10),0):0;
	putchar((x%10)^48);
}
template<typename TP> inline void writeln(TP x)
{
	write<TP>(x);
	puts("");
}
struct custom_hash
{
	static uint64_t splitmix64(uint64_t x)
	{
		x+=0x9e3779b97f4a7c15;
		x=(x^(x>>30))*0xbf58476d1ce4e5b9;
		x=(x^(x>>27))*0x94d049bb133111eb;
		return x^(x>>31);
	}
	size_t operator()(uint64_t x) const
	{
		static const uint64_t FIXED_RANDOM=chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x+FIXED_RANDOM);
	}
};
struct dsu1
{
	vector<int> fa;
	vector<unordered_map<int,pair<int,int>,custom_hash>> mp;
	vector<unordered_set<int,custom_hash>> rev;
	int &cnt;
	dsu1(int _n,int &_cnt):fa(_n+1),mp(_n+1),rev(_n+1),cnt(_cnt){iota(fa.begin(),fa.end(),0);}
	int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
	inline void merge(int u,int v)
	{
		int fu=find(u),fv=find(v);
		if(fu==fv) return;
		if(mp[fu].size()<mp[fv].size()) swap(fu,fv);
		for(auto [z,_]:mp[fv])
		{
			auto [x,y]=_;
			auto it=mp[fu].find(z);
			int xx=0,yy=0;
			if(it!=mp[fu].end()) tie(xx,yy)=it->second;
			int oldv=min(x,y)+min(xx,yy),newv=min(x+xx,y+yy);
			cnt+=newv-oldv,mp[fu][z]={x+xx,y+yy};
			rev[z].erase(fv),rev[z].insert(fu);
		}
		mp[fv].clear();
		fa[fv]=fu;
	}
};
struct dsu2
{
	vector<int> fa;
	vector<unordered_set<int,custom_hash>> *rev;
	vector<unordered_map<int,pair<int,int>,custom_hash>> *mp;
	int &cnt;
	dsu2(int _n,vector<unordered_set<int,custom_hash>> *_rev,vector<unordered_map<int,pair<int,int>,custom_hash>> *_mp,int &_cnt):fa(_n+1),rev(_rev),mp(_mp),cnt(_cnt){iota(fa.begin(),fa.end(),0);}
	int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
	inline void merge(int u,int v)
	{
		int fu=find(u),fv=find(v);
		if(fu==fv) return;
		if((*rev)[fu].size()<(*rev)[fv].size()) swap(fu,fv);
		for(auto z:(*rev)[fv])
		{
			auto itu=(*mp)[z].find(fu),itv=(*mp)[z].find(fv);
			int val1=itu==(*mp)[z].end()?0:itu->second.first;
			int val2=itu==(*mp)[z].end()?0:itu->second.second;
			int val3=itv==(*mp)[z].end()?0:itv->second.first;
			int val4=itv==(*mp)[z].end()?0:itv->second.second;
			int oldv=min(val1,val2)+min(val3,val4),newv=min(val1+val3,val2+val4);
			cnt+=newv-oldv,(*mp)[z][fu]={val1+val3,val2+val4};
			(*mp)[z].erase(fv),(*rev)[fu].insert(z);
		}
		(*rev)[fv].clear();
		fa[fv]=fu;
	}
};
int n,a[100001],b[100001],p[100001],posa[100001],posb[100001],ans[100001];
signed main()
{
	read(n);
	rep(i,1,n) read(a[i]),posa[a[i]]=i;
	rep(i,1,n) read(b[i]),posb[b[i]]=i;
	rep(i,1,n) read(p[i]);
	int cnt=0; dsu1 d1(n,cnt);
	rep(i,1,n) d1.mp[i][i]={1,0},d1.rev[i].insert(i);
	rep(i,1,n)
	{
		int u=posa[i],v=posb[p[i]];
		if(!d1.mp[u].count(v)) d1.mp[u][v]={0,0},d1.rev[v].insert(u);
		++d1.mp[u][v].second;
	}
	rep(i,1,n)
	{
		auto it=d1.mp[i].find(i);
		if(it!=d1.mp[i].end()) cnt+=min(it->second.first,it->second.second);
	}
	dsu2 d2(n,&d1.rev,&d1.mp,cnt);
	vector<pair<int,int>> e1,e2;
	rep(i,1,n-1) e1.emplace_back(max(a[i],a[i+1]),i),e2.emplace_back(max(b[i],b[i+1]),i);
	sort(e1.begin(),e1.end()),sort(e2.begin(),e2.end());
	int ptr1=0,ptr2=0;
	rep(i,1,n)
	{
		while(ptr1<(int)e1.size()&&e1[ptr1].first<=i) d1.merge(e1[ptr1].second,e1[ptr1].second+1),++ptr1;
		while(ptr2<(int)e2.size()&&e2[ptr2].first<=i) d2.merge(e2[ptr2].second,e2[ptr2].second+1),++ptr2;
		ans[i]=cnt;
	}
	rep(i,1,n) write(ans[i]),putchar('\n');
	return 0;
}