#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

#include <bits/stdc++.h>
using namespace std;

//fast IO by yosupo
//sc.read(string) だと append される
struct Scanner {
    FILE* fp = nullptr;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += fread(line + ed, 1, (1 << 15) - ed, fp);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) reread();
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        ref.clear();
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();            
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] - '0');
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(vector<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    Scanner(FILE* _fp) : fp(_fp) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val;  // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char('0' + (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }
    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const vector<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
    void write_single(long double d){
		{
			long long v=d;
			write_single(v);
			d-=v;
		}
		write_single('.');
		for(int _=0;_<8;_++){
			d*=10;
			long long v=d;
			write_single(v);
			d-=v;
		}
    }
};

Scanner sc(stdin);
Printer pr(stdout);

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t>
void print_single(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

template<class T>
void print_single(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print_single(v[i],i==int(v.size())-1?suc:2);
}

template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
	rep(i,v.size())
		print_single(v[i]+off,i==int(v.size())-1?suc:2);
}

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}*/
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int topbit(ull t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+1);
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	//#ifdef LOCAL
	static mt19937_64 gen;
	/*#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif*/
	return uniform_int_distribution<ll>(l, r)(gen);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}
template<class t>
bool bis(const vc<t>&v,const t&a){
	return binary_search(all(v),a);
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

template<class t>
vc<t> presum(const vc<t>&a){
	vc<t> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
pair<t,int> MAXi(const vc<t>&a){
	auto itr=max_element(all(a));
	return mp(*itr,itr-a.bg);
}

template<class t>
t MIN(const vc<t>&a){
	return *min_element(all(a));
}

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
void soin(S&s){
	sort(all(s));
}

template<class S>
S soout(S s){
	soin(s);
	return s;
}

template<class S>
void rein(S&s){
	reverse(all(s));
}

template<class S>
S reout(S s){
	rein(s);
	return s;
}

template<class t,class u>
pair<t,u>&operator+=(pair<t,u>&a,pair<t,u> b){
	a.a+=b.a;a.b+=b.b;return a;}
template<class t,class u>
pair<t,u>&operator-=(pair<t,u>&a,pair<t,u> b){
	a.a-=b.a;a.b-=b.b;return a;}
template<class t,class u>
pair<t,u> operator+(pair<t,u> a,pair<t,u> b){return mp(a.a+b.a,a.b+b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a,pair<t,u> b){return mp(a.a-b.a,a.b-b.b);}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

template<class t>
void pb(vc<t>&a,const vc<t>&b){
	a.insert(a.ed,all(b));
}

template<class t>
vc<t> cat(vc<t> a,const vc<t>&b){
	pb(a,b);
	return a;
}

template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
	for(auto&v:a)v+=x;
	return a;
}

template<class t,class u>
vc<t> operator+(vc<t> a,u x){
	return a+=x;
}

template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
	for(auto&v:a)v-=x;
	return a;
}

template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
	return a-=x;
}

//#define PAVLLAZY
//S_ bytes のバッファを確保
//ARC030D
//Copy and Paste
//FHC 2022 Round3 E2
//https://qiita.com/QCFium/items/3cf26a6dc2d49ef490d7
template<class N,int S_>
struct pavl{
	struct N2{
		using np=N2*;
		N v;
		np l,r;
		int h;
		//h は葉までの最長パスのノード数
		//null node で 0
		//v has no lazy data
		np upd(){
			v.single();
			h=0;
			if(l){
				v.updatel(l->v);
				chmax(h,l->h);
			}
			if(r){
				v.updater(r->v);
				chmax(h,r->h);
			}
			h++;
			return this;
		}
		np L(np x){l=x;return upd();}
		np R(np x){r=x;return upd();}
		np LR(np x,np y){l=x;r=y;return upd();}
	};
	static constexpr int S=S_/sizeof(N2);
	N2 buf[S];
	using np=N2*;
	int fix=0,used=0;
	np nn(N v){
		assert(used<S);
		buf[used]=N2{v,0,0,1};
		return buf+used++;
	}
	//a is not null
	np clone(np&a){
		if(a-buf<fix){
			assert(used<S);
			buf[used]=*a;
			a=buf+used++;
		}
		return a;
	}
	//a is not null
	np push(np&x){
		clone(x);
		#ifdef PAVLLAZY
		if(x->l)x->v.push(clone(x->l)->v);
		if(x->r)x->v.push(clone(x->r)->v);
		x->v.clear();
		#endif
		return x;
	}
	int hei(np x){return x?x->h:0;}
	N val(np x){return x?x->v:N();}
	int ok(int a,int b){return abs(a-b)<=1;}
	//x is already cloned
	//x needs upd
	//hei(res)==max(hei(x->l),hei(x->r))+(0 or 1)
	//O(|hei(x->r)-hei(x->r)|)
	np balance(np x){
		np a=x->l;
		np b=x->r;
		int dif=hei(a)-hei(b);
		if(inc(-1,dif,1)){
			return x->upd();
		}else if(dif<0){
			push(b);
			if(dif<-2){
				return Lb(b,Rb(x,b->l));
			}else if(ok(hei(b->l)+1,hei(b->r))){
				return b->L(x->R(b->l));
			}else{
				np y=push(b->l);
				return y->LR(x->R(y->l),b->L(y->r));
			}
		}else if(dif>0){
			push(a);
			if(dif>2){
				return Rb(a,Lb(x,a->r));
			}else if(ok(hei(a->l),hei(a->r)+1)){
				return a->R(x->L(a->r));
			}else{
				np y=push(a->r);
				return y->LR(a->R(y->l),x->L(y->r));
			}
		}else assert(false);
	}
	np Lb(np x,np a){x->l=a;return balance(x);}
	np Rb(np x,np a){x->r=a;return balance(x);}
	//hei(res)==max(hei(a),hei(b))+(0 or 1)
	//O(hei(a)+hei(b))
	np mergedfs(np a,np b){
		if(a==0)return b;
		if(b==0)return a;
		if(hei(a)<hei(b)){
			push(b);
			return Lb(b,mergedfs(a,b->l));
		}else{
			push(a);
			return Rb(a,mergedfs(a->r,b));
		}
	}
	template<class...Args>
	np merge(Args...args){
		fix=used;
		np res=0;
		for(auto x:{args...})res=mergedfs(res,x);
		return res;
	}
	template <class F,class... Args> 
	pair<np,np> max_right(np x,N cur,F f,Args&&... args){
		if(x==0)return mp(np(0),np(0));
		push(x);
		x->v.single();
		N nx=cur;
		nx.updater(val(x->l));
		nx.updater(val(x));
		if((nx.*f)(forward<Args>(args)...)){
			auto [a,b]=max_right(x->r,nx,f,forward<Args>(args)...);
			return mp(Rb(x,a),b);
		}else{
			auto [a,b]=max_right(x->l,cur,f,forward<Args>(args)...);
			return mp(a,Lb(x,b));
		}
	}
	template <class F,class... Args> 
	pair<np,np> max_right(np x,F f,Args&&... args){
		fix=used;
		return max_right(x,N(),f,forward<Args>(args)...);
	}
	//f(v,args)=true が左，false が右
	//not verified
	/*template <class F,class... Args>
	pair<np,np> split_by_cmp(np x,F f,Args&&... args){
		if(x==0)return mp(np(0),np(0));
		push(x);
		x->v.single();
		if(f(x->v,forward<Args>(args)...)){
			auto [a,b]=split_by_cmp(x->r,f,forward<Args>(args)...);
			return mp(Rb(x,a),b);
		}else{
			auto [a,b]=split_by_cmp(x->l,f,forward<Args>(args)...);
			return mp(a,Lb(x,b));
		}
	}*/
	//lower_bound の位置に insert
	//FHC 2022 Round3 E2 (without LAZY)
	template <class F>
	np insertdfs(np x,F f,const N&v){
		if(x==0)return nn(v);
		push(x);
		x->v.single();
		if(f(x->v,v)){
			return Rb(x,insertdfs(x->r,f,v));
		}else{
			return Lb(x,insertdfs(x->l,f,v));
		}
	}
	template <class F>
	np insert_by_cmp(np x,F f,const N&v){
		fix=used;
		return insertdfs(x,f,v);
	}
	//lower_bound の位置を erase
	//erase が実際に走ったかどうかが bool で返る
	//FHC 2022 Round3 E2 (without LAZY, all true)
	template <class F>
	pair<bool,np> erasedfs(np x,F f,const N&v){
		if(x==0)return mp(false,np(0));
		push(x);
		x->v.single();
		if(f(x->v,v)){
			auto [done,y]=erasedfs(x->r,f,v);
			return mp(done,Rb(x,y));
		}else{
			auto [done,y]=erasedfs(x->l,f,v);
			if(done)return mp(true,Lb(x,y));
			else return mp(true,merge(y,x->r));
		}
	}
	template <class F>
	pair<bool,np> erase_by_cmp(np x,F f,const N&v){
		fix=used;
		return erasedfs(x,f,v);
	}
	//lower_bound が存在するかどうかを bool で返す
	//存在するならノード情報も返す
	//FHC 2022 Round3 E2 (without LAZY)
	template <class F>
	pair<bool,N> lower_bound_by_cmp(np x,F f,N v){
		fix=used;
		np res=0;
		while(x){
			push(x);
			x->v.single();
			if(f(x->v,v)){
				x=x->r;
			}else{
				res=x;
				x=x->l;
			}
		}
		used=fix;
		if(res)return mp(true,res->v);
		else return mp(false,N());
	}
	np insert(np x,const N&v){return insert_by_cmp(x,less<N>(),v);}
	pair<bool,np> erase(np x,const N&v){return erase_by_cmp(x,less<N>(),v);}
	pair<bool,N> lower_bound(np x,const N&v){return lower_bound_by_cmp(x,less<N>(),v);}
	void clear(){fix=used=0;}
	template<class T>
	np build(const T&rw){
		fix=used;
		auto dfs=[&](auto self,int l,int r)->np{
			if(l==r)return 0;
			int m=(l+r)/2;
			np x=nn(rw[m]);
			return x->LR(self(self,l,m),self(self,m+1,r));
		};
		return dfs(dfs,0,si(rw));
	}
	vc<N> listup(np root){
		fix=used;
		vc<N> res;
		auto dfs=[&](auto self,np x)->void{
			if(x==0)return;
			push(x);
			self(self,x->l);
			res.pb(x->v);
			self(self,x->r);
		};
		dfs(dfs,root);
		return res;
	}
	void rebuild_if_needed(np&x,int maxlen){
		if(used+1000+maxlen>S){
			auto ls=listup(x);
			clear();
			x=build(ls);
		}
	}
};
//デフォルトコンストラクターが null node になっているべき (例えば len=0)
//reverse なし
//N::push
//副作用なし,１個の子にpush
//N::clear
//lazy tagを消去
//push/lazy は PAVLAZY がdefineされてなければ呼ばれない（これ定数倍変わる？）
//N::single
//ノード単体の情報を元に部分木情報を初期化
//N::updatel,updater
//N::ok
//max_right のノリで split をする
//ノード同士の比較関数でも split 可能(TODO)
//TODO 細かい実装の違いによる定数倍を検証

//Copy and Paste
template<class t>
struct SingleElement{
	t val;
	int len;
	SingleElement():val(0),len(0){}
	SingleElement(t v):val(v),len(1){}
	void single(){
		len=1;
	}
	void upd(const SingleElement&x){
		len+=x.len;
	}
	void updatel(const SingleElement&x){upd(x);}
	void updater(const SingleElement&x){upd(x);}
	bool ok_len(int x){
		return len<=x;
	}
};
using N=SingleElement<char>;

pavl<N,1400*ten(6)> t;
using np=decltype(t)::np;

//https://stackoverflow.com/a/49091681
template<class Tuple>
auto tuple_pop_front(Tuple tuple) {
	return apply([](auto a,auto...rest){return mp(a,mt(rest...));},tuple);
}
tuple<np> cut_by_index(np a){
	return a;
}
template<class...Args>
auto cut_by_index(np x,int pos,Args...args){
	assert((!x&&pos==0)||inc(0,pos,x->v.len));
	auto [ab,c]=tuple_pop_front(cut_by_index(x,args...));
	return tuple_cat(t.max_right(ab,&N::ok_len,pos),c);
}

bool dbg=false;

np slv(string raw,bool isder){
	vc<np> roots{nullptr};
	int cur=0;
	np clip=nullptr;

	stringstream ss(raw);
	int n;ss>>n;
	
	auto insert=[&](){
		np root=roots[cur];
		
		int p;ss>>p;
		string s;ss>>s;
		auto [x,y]=cut_by_index(root,p);
		root=t.merge(x,t.build(s),y);
		
		roots.resize(++cur);
		roots.pb(root);
	};
	auto erase=[&](){
		np root=roots[cur];
		
		int l,r;ss>>l>>r;
		auto [x,y,z]=cut_by_index(root,l,r);
		root=t.merge(x,z);
		
		roots.resize(++cur);
		roots.pb(root);
	};
	auto copy=[&](){
		np root=roots[cur];
		
		int l,r;ss>>l>>r;
		auto [x,y,z]=cut_by_index(root,l,r);
		clip=y;
	};
	auto cut=[&](){
		np root=roots[cur];
		
		int l,r;ss>>l>>r;
		auto [x,y,z]=cut_by_index(root,l,r);
		root=t.merge(x,z);
		clip=y;
		
		roots.resize(++cur);
		roots.pb(root);
	};
	auto paste=[&](){
		np root=roots[cur];
		
		int p;ss>>p;
		auto [x,y]=cut_by_index(root,p);
		root=t.merge(x,clip,y);
		
		roots.resize(++cur);
		roots.pb(root);
	};
	auto print_ans=[&](){
		np root=roots[cur];
		
		int l,r;ss>>l>>r;
		if(isder)return;
		
		auto [x,y,z]=cut_by_index(root,l,r);
		auto ans=t.listup(y);
		
		for(auto c:ans)pr.write(c.val);
		pr.write("\n");
	};
	auto serialize=[&](){
		if(isder)return;
		
		//!0->space
		//!1->!
		string ser;
		for(auto c:raw){
			if(c==' '){
				ser+='!';
				ser+='0';
			}else if(c=='!'){
				ser+='!';
				ser+='1';
			}else{
				ser+=c;
			}
		}
		
		assert(si(ser)<=ten(7));
		pr.writeln(ser);
	};
	auto deserialize=[&](){
		string en;ss>>en;
		if(isder)return;
		
		string nx;
		for(int i=0;i<si(en);){
			char c=en[i];
			if(c=='!'){
				i++;
				if(en[i]=='0')nx+=' ';
				else if(en[i]=='1')nx+='!';
				else assert(0);
			}else{
				nx+=c;
			}
			i++;
		}
		
		np root=slv(nx,true);
		
		roots.resize(++cur);
		roots.pb(root);
	};
	rep(phase,n){
		string type;ss>>type;
		
		if(type=="insert"){
			insert();
		}else if(type=="erase"){
			erase();
		}else if(type=="print"){
			print_ans();
		}else if(type=="copy"){
			copy();
		}else if(type=="cut"){
			cut();
		}else if(type=="paste"){
			paste();
		}else if(type=="undo"){
			if(cur>0)cur--;
		}else if(type=="redo"){
			if(cur+1<si(roots))cur++;
		}else if(type=="serialize"){
			serialize();
		}else if(type=="deserialize"){
			deserialize();
		}else{
			dmp(type);
			//exit(0);
			assert(false);
		}
	}
	return roots[cur];
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	if(dbg){
		//while(1)slv();
	}else{
		//int t;cin>>t;rep(_,t)
		string raw;
		while(1){
			string s;
			if(sc.read_single(s)){
				raw+=" ";
				raw+=s;
			}
			else break;
		}
		slv(raw,false);
	}
}