#include using namespace std; using ll=long long; using ld=long double; using ull=unsigned long long; using uint=unsigned int; using pcc=pair; using pii=pair; using pll=pair; using pdd=pair; using tuplis=pair; using tuplis2=pair; template using pq=priority_queue,greater>; const ll LINF=0x1fffffffffffffff; const ll MINF=0x7fffffffffff; const int INF=0x3fffffff; const ll MOD=1000000007; const ll MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.141592653589793238462643383279; const vectorfour{0,1,0,-1,0}; #define _overload4(_1,_2,_3,_4,name,...) name #define _overload3(_1,_2,_3,name,...) name #define _rep1(n) for(ll i=0;i=0;i--) #define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--) #define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--) #define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c) #define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__) #define each(i,a) for(auto &i:a) #define sum(...) accumulate(range(__VA_ARGS__),0LL) #define dsum(...) accumulate(range(__VA_ARGS__),double(0)) #define _range(i) (i).begin(),(i).end() #define _range2(i,k) (i).begin(),(i).begin()+k #define _range3(i,a,b) (i).begin()+a,(i).begin()+b #define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__) #define _rrange(i) (i).rbegin(),(i).rend() #define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k #define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__) #define elif else if #define unless(a) if(!(a)) #define mp make_pair #define mt make_tuple #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vector name(__VA_ARGS__) #define VEC(type,name,size) vector name(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,...) vector>name(h,vector(__VA_ARGS__));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) inline constexpr ll gcd(ll a,ll b){if(!a||!b)return 0;while(b){ll c=b;b=a%b;a=c;}return a;} inline constexpr ll lcm(ll a,ll b){if(!a||!b)return 0;return a*b/gcd(a,b);} template inline constexpr T min(vector &v){return *min_element(range(v));} inline char min(string &v){return *min_element(range(v));} template inline constexpr T max(vector &v){return *max_element(range(v));} inline char max(string &v){return *max_element(range(v));} inline constexpr ll intpow(ll a,ll b){ll ans=1;for(ll i=1;b;i*=2){if(b&i){b^=i;ans*=a;}a*=a;}return ans;} template inline constexpr bool chmin(T &mn,const T &cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;} template inline constexpr bool chmax(T &mx,const T &cnt){if(mx unordered_map press(vector &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } template map press_map(vector &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } inline int scan(){ return getchar(); } inline void scan(int &a){ scanf("%d", &a); } inline void scan(unsigned &a){ scanf("%u", &a); } inline void scan(long &a){ scanf("%ld", &a); } inline void scan(long long &a){ scanf("%lld", &a); } inline void scan(unsigned long long &a){ scanf("%llu", &a); } inline void scan(char &a){ cin >> a; } inline void scan(float &a){ scanf("%f", &a); } inline void scan(double &a){ scanf("%lf", &a); } inline void scan(long double &a){ scanf("%Lf", &a); } inline void scan(vector &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } } inline void scan(char a[]){ scanf("%s", a); } inline void scan(string &a){ cin >> a; } template inline void scan(vector &vec); template inline void scan(array &vec); template inline void scan(pair &p); template inline void scan(T (&vec)[size]); template inline void scan(vector &vec){ for(auto &i : vec) scan(i); } template inline void scan(array &vec){ for(auto &i : vec) scan(i); } template inline void scan(pair &p){ scan(p.first); scan(p.second); } template inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); } template inline void scan(T &a){ cin>>a; } inline void in(){} template inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); } inline void print(){ putchar(' '); } inline void print(const bool &a){ printf("%d", a); } inline void print(const int &a){ printf("%d", a); } inline void print(const unsigned &a){ printf("%u", a); } inline void print(const long &a){ printf("%ld", a); } inline void print(const long long &a){ printf("%lld", a); } inline void print(const unsigned long long &a){ printf("%llu", a); } inline void print(const char &a){ printf("%c", a); } inline void print(const char a[]){ printf("%s", a); } inline void print(const float &a){ printf("%.15f", a); } inline void print(const double &a){ printf("%.15f", a); } inline void print(const long double &a){ printf("%.15Lf", a); } inline void print(const string &a){ each(i, a) print(i); } template void print(const vector &vec); template void print(const array &vec); template void print(const pair &p); template inline void print(const T (&vec)[size]); template void print(const vector &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template void print(const array &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template void print(const pair &p){ print(p.first); putchar(' '); print(p.second); } template inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } } template inline void print(const T &a){ cout << a; } inline int out(){ putchar('\n'); return 0; } template inline int out(const T &t){ print(t); putchar('\n'); return 0; } template inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } template inline void err(T t){cerr< inline void err(const Head &head, const Tail&... tail){ cerr<v; while(a){ v.push_back(a%c); a/=c; } if(v.back()==1){ v.pop_back(); v.back()+=c; } each(i,v){ if(i>(c-1)*2)i=3; elif(i>=c)i=2; elif(i)i=1; } out((sum(v)+v.size()-1)*b); } }