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

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

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);
}
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);
}

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

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

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

//mint107 は verify してねえ
//#define DYNAMIC_MOD

struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
	mod=m;
	im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
	ull z=ull(a)*b;
	uint x=((unsigned __int128)z*im)>>64;
	uint v=uint(z)-x*mod;
	return v<mod?v:v+mod;
}
#endif
};
template<modinfo const&ref>
struct modular{
	static constexpr uint const &mod=ref.mod;
	static modular root(){return modular(ref.root);}
	uint v;
	//modular(initializer_list<uint>ls):v(*ls.bg){}
	modular(ll vv=0){s(vv%mod+mod);}
	modular& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	modular operator-()const{return modular()-*this;}
	modular& operator+=(const modular&rhs){return s(v+rhs.v);}
	modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
	modular&operator*=(const modular&rhs){
		#ifndef DYNAMIC_MOD
		v=ull(v)*rhs.v%mod;
		#else
		v=ref.product(v,rhs.v);
		#endif
		return *this;
	}
	modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
	modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
	modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
	modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
	modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
	modular pow(ll n)const{
		if(n<0)return inv().pow(-n);
		modular res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	modular inv()const{return pow(mod-2);}
	/*modular inv()const{
		int x,y;
		int g=extgcd<ll>(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(ll x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(ll x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(ll x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(ll x,const modular&y){
		return modular(x)/y;
	}
	friend ostream& operator<<(ostream&os,const modular&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,modular&m){
		ll x;is>>x;
		m=modular(x);
		return is;
	}
	bool operator<(const modular&r)const{return v<r.v;}
	bool operator==(const modular&r)const{return v==r.v;}
	bool operator!=(const modular&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

#ifndef DYNAMIC_MOD
//extern constexpr modinfo base{998244353,3};
extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;

//ABC135F
//Yukicoder No.263
//https://codeforces.com/gym/103698/problem/H
namespace rhash{
	const int k=2;
	vc<array<mint,k>> a,b;
	void init(int n){
		a.resize(n+1);
		b.resize(n+1);
		rep(i,k){
			a[0][i]=1;
			a[1][i]=rand_int(1,mint::mod-1);
			b[0][i]=1;
			b[1][i]=a[1][i].inv();
		}
		rng(i,1,n)
			rep(j,k){
				a[i+1][j]=a[i][j]*a[1][j];
				b[i+1][j]=b[i][j]*b[1][j];
			}
	}
	using P=pair<array<mint,k>,int>;
	P mrg(P x,const P&y){
		rep(i,k)
			x.a[i]+=y.a[i]*a[x.b][i];
		x.b+=y.b;
		return x;
	}
	template<class...Args>
	P mrg(const P&x,const P&y,Args...args){
		return mrg(mrg(x,y),forward<Args>(args)...);
	}
	//x is a prefix of y
	P dif(const P&x,P y){
		rep(i,k){
			y.a[i]-=x.a[i];
			y.a[i]*=b[x.b][i];
		}
		y.b-=x.b;
		return y;
	}
	template<class t>
	P single(t c){
		P res;
		res.b=1;
		rep(i,k)res.a[i]=c;
		return res;
	}
	P hpow(P p,int n){
		P res;
		while(n){
			if(n&1)res=mrg(res,p);
			p=mrg(p,p);
			n>>=1;
		}
		return res;
	}
	struct gen{
		gen(){}
		vc<array<mint,k>> c;
		template<class S>
		gen(S s):c(s.size()+1){
			rep(i,s.size())
				rep(j,k)
					c[i+1][j]=c[i][j]+a[i][j]*s[i];
		}
		P get(int l,int r){
			P res;
			rep(i,k)
				res.a[i]=(c[r][i]-c[l][i])*b[l][i];
			res.b=r-l;
			return res;
		}
	};
}


template<class t>
struct BIT{
	vc<t> buf;
	int s;
	BIT(int n=0){init(n);}
	BIT(const vc<t>&a){init(a);}
	void init(int n){buf.clear();buf.resize(s=n);}
	void init(const vc<t>&a){
		s=si(a);
		buf.resize(s);
		rep(i,s)buf[i]=a[i];
		rep(i,s){
			int j=i+((i+1)&(-i-1));
			if(j<s)buf[j]+=buf[i];
		}
	}
	void add(int i,t v){
		for(;i<s;i+=(i+1)&(-i-1))
			buf[i]+=v;
	}
	t get(int i){
		t res=t();
		for(;i>=0;i-=(i+1)&(-i-1))
			res+=buf[i];
		return res;
	}
	t sum(int b,int e){
		return get(e-1)-get(b-1);
	}
	void add_range(int b,int e,t v){
		add(b,v);
		add(e,-v);
	}
	int kth(int k){
		int res=0;
		for(int i=topbit(s);i>=0;i--){
			int w=res+(1<<i);
			if(w<=s&&buf[w-1]<=k){
				k-=buf[w-1];
				res=w;
			}
		}
		return res;
	}
	//yukicoder No.1024
	int kth_helper(int k,int i){
		return kth(k+get(i-1));
	}
};

//主客転倒
//長方形領域に加算，点取得
//query のソート関数が微妙にほかと違う
struct point2d{
	struct query{
		int x,i,l,r;
		bool operator<(const query&rhs)const{
			return pi(x,i)<pi(rhs.x,rhs.i);
		}
	};
	vi ys,ans;
	vc<query> qs;
	point2d(const vc<pi>&ps){
		for(auto p:ps)
			ys.pb(p.b);
		mkuni(ys);
		ans.resize(si(ps));
		rep(i,si(ps))
			qs.pb({ps[i].a,inf+i,lwb(ys,ps[i].b),-1});
	}
	void aq(int x1,int x2,int y1,int y2,int w){
		y1=lwb(ys,y1);
		y2=lwb(ys,y2);
		qs.pb({x1,w,y1,y2});
		qs.pb({x2,-w,y1,y2});
	}
	vi calc(){
		sort(all(qs));
		BIT<int> bit(si(ys));
		for(auto q:qs){
			if(q.i<inf){
				bit.add_range(q.l,q.r,q.i);
			}else{
				ans[q.i-inf]=bit.get(q.l);
			}
		}
		return ans;
	}
};

//O(N+max(A)) なので座標圧縮してから動かしてください
//Verify yosupo (N=500000,string,43ms)
template<class t>vi sais(t a){
	int n=si(a),m=*max_element(all(a))+1;
	vi pos(m+1),x(m),sa(n),val(n),lms;
	for(auto c:a)pos[c+1]++;
	rep(i,m)pos[i+1]+=pos[i];
	vc<bool> s(n);
	per(i,n-1)s[i]=a[i]!=a[i+1]?a[i]<a[i+1]:s[i+1];
	auto ind=[&](const vi&ls){
		fill(all(sa),-1);
		auto L=[&](int i){if(i>=0&&!s[i])sa[x[a[i]]++]=i;};
		auto S=[&](int i){if(i>=0&& s[i])sa[--x[a[i]]]=i;};
		rep(i,m)x[i]=pos[i+1];
		per(i,si(ls))S(ls[i]);
		rep(i,m)x[i]=pos[i];
		L(n-1);
		rep(i,n)L(sa[i]-1);
		rep(i,m)x[i]=pos[i+1];
		per(i,n)S(sa[i]-1);
	};
	auto ok=[&](int i){return i==n||(!s[i-1]&&s[i]);};
	auto same=[&](int i,int j){
		do{
			if(a[i++]!=a[j++])return false;
		}while(!ok(i)&&!ok(j));
		return ok(i)&&ok(j);
	};
	rng(i,1,n)if(ok(i))lms.pb(i);
	ind(lms);
	if(si(lms)){
		int p=-1,w=0;
		for(auto v:sa)if(v&&ok(v)){
			if(p!=-1&&same(p,v))w--;
			val[p=v]=w++;
		}
		vi b=lms;
		for(auto&v:b)v=val[v];
		b=sais(b);
		for(auto&v:b)v=lms[v];
		ind(b);
	}
	return sa;
}

struct SA{
	int n;
	vi sa,as,lcp;
	template<class t> SA(t s):n(si(s)),as(n),lcp(n-1){
		/*{//座標圧縮,値域が小さいなら skip 可
			auto vs=s;mkuni(vs);
			for(auto&v:s)v=lwb(vs,v);
		}*/
		sa=sais(s);
		//as
		rep(i,n)as[sa[i]]=i;
		//lcp
		int w=0;
		for(auto i:as){
			if(w)w--;
			if(i<n-1){
				while(max(sa[i],sa[i+1])+w<n&&s[sa[i]+w]==s[sa[i+1]+w]) w++;
				lcp[i]=w;
			}
		}
	}
};

//N() が単位元
//VERIFY: yosupo
//CF407E
template<class N>
struct segtree{
	vc<N> x;
	int s;
	segtree(){}
	template<class t>
	segtree(vc<t> a){
		int n=a.size();
		s=1;
		while(s<n){s*=2;}
		x.resize(s*2);
		rep(i,n)
			x[s+i]=N(a[i]);
		gnr(i,1,s)
			x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	//NOT Verified
	segtree(int n){
		resize(n);
	}
	void resize(int n){
		s=1;
		while(s<n){s*=2;}
		x.assign(s*2,N());
		gnr(i,1,s)
			x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	N point_get(int i){
		return x[i+s];
	}
	void point_set(int i,const N&t){
		i+=s;
		x[i]=t;
		while(i>>=1)x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	void point_merge(int i,const N&t){
		i+=s;
		x[i]=N::merge(x[i],t);
		while(i>>=1)x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	template<class F,class...Args>
	void point_change(int i,F f,Args&&...args){
		i+=s;
		(x[i].*f)(forward<Args>(args)...);
		while(i>>=1)x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	N composite(int b,int e){
		assert(b<=e);
		N lf,rt;
		for(int l=b+s,r=e+s;l<r;l>>=1,r>>=1){
			if (l&1){
				lf=N::merge(lf,x[l]);
				l++;
			}
			if (r&1){
				r--;
				rt=N::merge(x[r],rt);
			}
		}
		return N::merge(lf,rt);
	}
	N getall(){
		return x[1];
	}
	//UTPC2020E
	//n 超えるかもしれない
	template <class F,class... Args> 
	pair<int,N> max_right(int l,F f,Args&&... args){
		assert(0<=l&&l<=s);
		if(l==s)return mp(s,N());
		l+=s;
		
		N sm;
		assert((sm.*f)(forward<Args>(args)...));
		do {
			while (l % 2 == 0) l >>= 1;
			if (!(N::merge(sm,x[l]).*f)(forward<Args>(args)...)){
				while (l < s) {
					l = (2 * l);
					N tmp=N::merge(sm,x[l]);
					if ((tmp.*f)(forward<Args>(args)...)) {
						sm = tmp;
						l++;
					}
				}
				return mp(l - s,sm);
			}
			sm = N::merge(sm, x[l]);
			l++;
		} while ((l & -l) != l);
		return mp(s,sm);
	}
	//UTPC2020E
	template <class F,class... Args> 
	pair<int,N> min_left(int r,F f,Args&&... args){
		assert((N().*f)(forward<Args>(args)...));
		assert(0<=r&&r<=s);
        if(r==0)return mp(0,N());
        r+=s;
        N sm;
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!(N::merge(x[r],sm).*f)(forward<Args>(args)...)) {
                while (r < s) {
                    r = (2 * r + 1);
                    N tmp=N::merge(x[r],sm);
                    if ((tmp.*f)(forward<Args>(args)...)) {
                        sm = tmp;
                        r--;
                    }
                }
                return mp(r + 1 - s,sm);
            }
            sm = N::merge(x[r], sm);
        } while ((r & -r) != r);
        return mp(0,sm);
    }
    //行列とか乗せて必要なのはベクトルとの積，みたいなときに使える？
    //CF Goodbye 2016 E
	template<class F,class T>
	T accumulate(int l, int r,F f,T t) {
		assert(0<=l&&l<=r&&r<=s);
		if (l == r) return t;

		l+=s;
		r+=s;

		static int buf[2][30];
		int cnt[2]{};
		{
			int l2 = l, r2 = r;
			while (l < r) {
				if (l & 1){
					//(x[l++].*f)(forward<Args>(args)...);
					buf[0][cnt[0]++]=l++;
				}
				if (r & 1){
					//(x[--r].*f)(forward<Args>(args)...);
					buf[1][cnt[1]++]=--r;
				}
				l >>= 1;
				r >>= 1;
			}
			l = l2;
			r = r2;
		}
		rep(i,cnt[0])t=(x[buf[0][i]].*f)(t);
		per(i,cnt[1])t=(x[buf[1][i]].*f)(t);

		return t;
	}
};

struct MinNode{
	int v;
	MinNode(int vv=inf):v(vv){}
	static MinNode merge(const MinNode&a,const MinNode&b){
		return MinNode(min(a.v,b.v));
	}
	bool ok(int x){return x<=v;}
};

string getrev(string s){
	reverse(all(s));
	return s;
}

void slv(){
	string s,t,p;cin>>s>>t>>p;
	rhash::init(si(s)+si(t)+si(p));
	auto sg=rhash::gen(s);
	auto tg=rhash::gen(t);
	auto pg=rhash::gen(p);
	int n=si(s),m=si(t),o=si(p);
	vi ans(n+1);
	{//only s
		auto tar=pg.get(0,o);
		rep(i,n-o+1)if(sg.get(i,i+o)==tar){
			//[0..i]
			//[i+o..n]
			ans[0]++;
			ans[i+1]--;
			ans[i+o]++;
		}
	}
	{//only t
		auto tar=pg.get(0,o);
		rep(i,m-o+1)if(tg.get(i,i+o)==tar)
			ans[0]++;
	}
	rep(i,n)ans[i+1]+=ans[i];
	SA sa(s+"$"+p);
	segtree<MinNode> seg(sa.lcp);
	SA saR(getrev(s)+"$"+getrev(p));
	segtree<MinNode> segR(saR.lcp);
	
	vc<pi> qls;
	rep(i,n+1)qls.eb(sa.as[i],saR.as[n-i]);
	point2d p2d(qls);
	
	auto getxlr=[&](int y){
		int pos=sa.as[n+1+(o-y)];
		int xl=seg.min_left(pos,&MinNode::ok,y).a;
		int xr=seg.max_right(pos,&MinNode::ok,y).a;
		return pi(xl,xr+1);
	};
	auto getylr=[&](int x){
		int pos=saR.as[n+1+(o-x)];
		int yl=segR.min_left(pos,&MinNode::ok,x).a;
		int yr=segR.max_right(pos,&MinNode::ok,x).a;
		return pi(yl,yr+1);
	};
	
	{//s1-t
		rng(y,1,o){
			int x=o-y;
			if(y<=m&&tg.get(0,y)==pg.get(x,o)){
				auto [yl,yr]=getylr(x);
				p2d.aq(-inf,inf,yl,yr,1);
			}
		}
	}
	{//t-s2
		rng(x,1,o){
			int y=o-x;
			if(x<=m&&tg.get(m-x,m)==pg.get(0,x)){
				auto [xl,xr]=getxlr(y);
				dmp2(x,xl,xr);
				p2d.aq(xl,xr,-inf,inf,1);
			}
		}
	}
	{
		rng(x,1,o-m){
			int y=o-m-x;
			if(tg.get(0,m)==pg.get(x,x+m)){
				auto [xl,xr]=getxlr(y);
				auto [yl,yr]=getylr(x);
				p2d.aq(xl,xr,yl,yr,1);
			}
		}
	}
	
	vi val=p2d.calc();
	rep(i,n+1)ans[i]+=val[i];
	dmp(ans);
	
	int maxval=MAX(ans);
	vi idx;
	rep(i,n+1)if(ans[i]==maxval)idx.pb(i);
	print(maxval,si(idx),idx[0],idx.back());
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	//int t;cin>>t;rep(_,t)
	slv();
}