Submission #47535130

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Source Code Expand

#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);
}
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,class u>
int lwb(const vc<t>&v,const u&a){
	return lower_bound(all(v),a)-v.bg;
}
template<class t,class u>
bool bis(const vc<t>&v,const u&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,class u>
void pb(vc<t>&a,const vc<u>&b){
	a.insert(a.ed,all(b));
}

template<class t,class...Args>
vc<t> cat(vc<t> a,Args&&...b){
	(pb(a,forward<Args>(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;
}

template<class t,class u>
void remval(vc<t>&a,const u&v){
	a.erase(remove(all(a),v),a.ed);
}

template<class t,class u>
void fila(vc<t>&vs,const u&a){
	fill(all(vs),a);
}

bool dbg=false;

//N() が単位元
//VERIFY: yosupo
//CF407E
template<class N>
struct segtree{
	vc<N> x;
	int n,s;
	segtree(){}
	template<class t>
	segtree(const vc<t>&a){
		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 nn){
		resize(nn);
	}
	void resize(int nn){
		n=nn;
		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]);
	}
	template<class t>
	void load(const vc<t>&a){
		n=a.size();
		s=1;
		while(s<n){s*=2;}
		x.resize(s*2);
		rep(i,n)
			x[s+i]=N(a[i]);
		rng(i,n,s)
			x[s+i]=N();
		gnr(i,1,s)
			x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	void clear(){
		rep(i,n)
			x[s+i]=N();
		gnr(i,1,s)
			x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	N point_get(int i){
		assert(inc(0,i,n-1));
		return x[i+s];
	}
	void point_set(int i,const N&t){
		assert(inc(0,i,n-1));
		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){
		assert(inc(0,i,n-1));
		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){
		assert(inc(0,i,n-1));
		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(0<=b&&b<=e&&e<=n);
		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((N().*f)(forward<Args>(args)...));
		assert(0<=l&&l<=n);
		if(l==n)return mp(n,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(n,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<=n);
        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
    //CF 896 F
	template<class F,class T,class... Args>
	T accumulate(int l,int r,F f,T t,Args&&... args) {
		assert(0<=l&&l<=r&&r<=n);
		static int buf[2][30];
		int cnt[2]{};
		for(l+=s,r+=s;l<r;l>>=1,r>>=1){
			if(l&1)buf[0][cnt[0]++]=l;
			if(r&1)buf[1][cnt[1]++]=r-1;
			l++;
		}
		rep(i,cnt[0])t=(x[buf[0][i]].*f)(t,forward<Args>(args)...);
		per(i,cnt[1])t=(x[buf[1][i]].*f)(t,forward<Args>(args)...);
		return t;
	}
};

//atcoder-library をまあまあコピーして使っている

//N() が単位元

//merge で片方が inactive のときはもう片方をそのまま返す，
//といったときに，lazy の情報までコピーして渡さないようにする

//クエリできる点が[0,s)だったのを[0,n)に変えた (UCUP1-21D)
//ch,max_rightは動くと思う
//ちゃんと test してないから assert とかが壊れたらごめん

//VERIFY:
//https://atcoder.jp/contests/practice2/tasks/practice2_k
template<class N,bool Beats=false>
struct seglazy{
	vc<N> x;
	int n,L,s;
	seglazy(){}
	template<class T>
	seglazy(const vc<T>& a){
		n=a.size();
		L=0;
		while((1<<L)<n)L++;
		s=1<<L;
		x.resize(s*2);
		rep(i,n)x[s+i]=N(a[i]);
		gnr(i,1,s)upd(i);
	}
	seglazy(int nn){
		n=nn;
		L=0;
		while((1<<L)<n)L++;
		s=1<<L;
		x.assign(s*2,N());
		gnr(i,1,s)upd(i);
	}
	void upd(int i){
		x[i]=N::merge(x[i*2],x[i*2+1]);
	}
	void push(int i){
		x[i].push(x[i*2],x[i*2+1]);
	}
	N composite(int l,int r){
		assert(0<=l&&l<=r&&r<=n);
		if(l==r)return N();
		
		l+=s;
		r+=s;
		
		for (int i = L; i >= 1; i--) {
			if (((l >> i) << i) != l) push(l >> i);
			if (((r >> i) << i) != r) push((r - 1) >> i);
		}
		
		N sml,smr;
		while (l < r) {
			if (l & 1) sml = N::merge(sml, x[l++]);
			if (r & 1) smr = N::merge(x[--r], smr);
			l >>= 1;
			r >>= 1;
		}

		return N::merge(sml, smr);
	}
	//UCUP1-21 D
	template<class F,class... Args>
	void ch_beats(int i,F f,Args&&... args){
		if((x[i].*f)(forward<Args>(args)...))return;
		push(i);
		ch_beats(i*2,f,forward<Args>(args)...);
		ch_beats(i*2+1,f,forward<Args>(args)...);
		upd(i);
	}
	template<class F,class... Args>
	void ch(int l, int r, F f,Args&&... args) {
		assert(0<=l&&l<=r&&r<=n);
		if (l == r) return;

		l+=s;
		r+=s;

		for (int i = L; i >= 1; i--) {
			if (((l >> i) << i) != l) push(l >> i);
			if (((r >> i) << i) != r) push((r - 1) >> i);
		}
		
		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;
		}
		if constexpr(Beats){
			rep(i,cnt[0])ch_beats(buf[0][i],f,forward<Args>(args)...);
			per(i,cnt[1])ch_beats(buf[1][i],f,forward<Args>(args)...);
		}else{
			rep(i,cnt[0])(x[buf[0][i]].*f)(forward<Args>(args)...);
			per(i,cnt[1])(x[buf[1][i]].*f)(forward<Args>(args)...);
		}

		for (int i = 1; i <= L; i++) {
			if (((l >> i) << i) != l) upd(l >> i);
			if (((r >> i) << i) != r) upd((r - 1) >> i);
		}
	}
	template<class F,class... Args>
	void chall(F f,Args&&... args){
		if constexpr(Beats){
			ch_beats(1,f,forward<Args>(args)...);
		}else{
			(x[1].*f)(forward<Args>(args)...);
		}
	}
	N getall(){return x[1];}
	template <class F,class... Args> 
	pair<int,N> max_right(int l,F f,Args&&... args){
		assert(0<=l&&l<=n);
		if(l==n)return mp(n,N());
		l+=s;
		
		for (int i = L; i >= 1; i--) push(l >> i);
		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) {
					push(l);
					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(n,sm);
	}
	//XXI Opencup Krakow M
	template <class F,class... Args> 
	pair<int,N> min_left(int r,F f,Args&&... args){
		assert(0<=r&&r<=n);
        if(r==0)return mp(0,N());
        r+=s;
        for (int i = L; i >= 1; i--) push((r - 1) >> i);
        N sm;
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!(N::merge(x[r],sm).*f)(forward<Args>(args)...)) {
                while (r < s) {
                    push(r);
                    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);
    }
	template<class F,class...Args>
	void point_change(int p,F f,Args&&...args){
		assert(0 <= p && p < n);
		p += s;
		for (int i = L; i >= 1; i--) push(p >> i);
		(x[p].*f)(forward<Args>(args)...);
		for (int i = 1; i <= L; i++) upd(p >> i);
	}
	void point_merge(int p,const N&t){
		assert(0 <= p && p < n);
		p += s;
		for (int i = L; i >= 1; i--) push(p >> i);
		x[p]=N::merge(x[p],t);
		for (int i = 1; i <= L; i++) upd(p >> i);
	}
	N point_get(int p){
		assert(0 <= p && p < n);
		p += s;
		for (int i = L; i >= 1; i--) push(p >> i);
		return x[p];
	}
	void point_set(int p,N val){
		assert(0 <= p && p < n);
		p += s;
		for (int i = L; i >= 1; i--) push(p >> i);
		x[p]=val;
		for (int i = 1; i <= L; i++) upd(p >> i);
	}
	void enumerater(int l,int r,int i,int b,int e,vc<N>&dst){
		if(e<=l||r<=b)
			return;
		if(l+1==r){
			dst.pb(x[i]);
			return;
		}
		push(i);
		int m=(l+r)/2;
		enumerater(l,m,i*2,b,e,dst);
		enumerater(m,r,i*2+1,b,e,dst);
	}
	void enumerate(int b,int e,vc<N>&dst){
		assert(0<=b&&b<=e&&e<=n);
		return enumerater(0,s,1,b,e,dst);
	}
};

//Range add,min
struct N{
	int lz,mn;
	N(int v=inf):lz(0),mn(v){}
	void add(int v){
		mn+=v;
		lz+=v;
	}
	void push(N&x,N&y){
		x.add(lz);
		y.add(lz);
		lz=0;
	}
	static N merge(N x,N y){
		return N(min(x.getm(),y.getm()));
	}
	int getm(){return mn;}
	bool ok(int v){
		return mn>v;
	}
};

struct MinNode{
	pi v;
	MinNode(pi vv=pi(inf,-1)):v(vv){}
	static MinNode merge(const MinNode&a,const MinNode&b){
		return MinNode(min(a.v,b.v));
	}
};

struct MaxNode{
	pi v;
	MaxNode(pi vv=pi(-inf,-1)):v(vv){}
	static MaxNode merge(const MaxNode&a,const MaxNode&b){
		return MaxNode(max(a.v,b.v));
	}
};

void slv(){
	int n,m,q;cin>>n>>m>>q;
	vi ini=readvi(n);
	vc<pi> xy(q);
	rep(i,q){
		int x,y;cin>>x>>y;
		x--;
		xy[i]=pi(x,y);
	}
	
	vi a(n);
	seglazy<N> flow(vi(n-1,0));
	vc<pi> tmp(n);
	rep(i,n)tmp[i]=pi(0,i);
	segtree<MinNode> incost(tmp);
	segtree<MaxNode> outcost(tmp);
	vi used(n,1);
	int ans=0;
	
	auto refresh=[&](int i){
		incost.point_set(i,pi(used[i]<2?a[i]:inf,i));
		outcost.point_set(i,pi(used[i]>0?a[i]:-inf,i));
	};
	
	auto pushflow=[&](int s,int t){
		assert(used[s]<2);
		used[s]++;
		refresh(s);
		ans-=a[s];
		
		assert(used[t]>0);
		used[t]--;
		refresh(t);
		ans+=a[t];
		
		if(s<t)flow.ch(s,t,&N::add,1);
		else flow.ch(t,s,&N::add,-1);
		assert(flow.getall().mn>=0);
	};
	
	auto upd=[&](int i,int v){
		ans+=(v-a[i])*(2-used[i]);
		a[i]=v;
		refresh(i);
		while(used[i]>0){
			int j=flow.max_right(i,&N::ok,0).a;
			auto [u,k]=incost.composite(0,j+1).v;
			if(u-v<0) pushflow(k,i);
			else break;
		}
		while(used[i]<2){
			int j=flow.min_left(i,&N::ok,0).a;
			auto [u,k]=outcost.composite(j,n).v;
			if(v-u<0) pushflow(i,k);
			else break;
		}
	};
	
	rep(i,n)upd(i,ini[i]);
	for(auto [x,y]:xy){
		upd(x,y);
		print(n*m-ans);
	}
}

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)
		slv();
	}
}

Submission Info

Judge Result