#include using namespace std; // -------------------------------------------------------------------------------------------------------------- //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") namespace VvyLw { void wa_haya_exe() { cin.tie(nullptr); ios::sync_with_stdio(false); } void solve(); }; // VvyLw mt19937 Random() { random_device seed_gen; mt19937 engine {seed_gen()}; return engine; } // -------------------------------------------------------------------------------------------------------------- template using V = vector; template using P = pair; template using pq = priority_queue; template using pqr = priority_queue,greater>; template using pqs = priority_queue>; template using pqrs = priority_queue,V>,greater>>; template bool chmax(T& a, const U& b) { if (a bool chmin(T& a, const U& b) { if (a>b) { a=b; return 1; } return 0; } template bool overflow_if_add(T a, U b) { return (numeric_limits::max()-a) bool overflow_if_mul(T a, U b) { return (numeric_limits::max()/a); using vu = V
    ; using vd = V; using vc = V; using vs = V; using vb = V; using wi = V; using wu = V; using wd = V; using wc = V; using ws = V; using wb = V; using pi = P; using pl = P; using pd = P; using pc = P; using ps = P; const int MOD = 998244353; const int M0D = 1000000007; const int INF = 0x3fffffff; const ll LINF = 0x1fffffffffffffff; const ld DINF = numeric_limits::infinity(); const double PI = acos(-1); #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 rvp2(i,n) for(ll i=n-1; i>=0; i--) #define rvp3(i,a,b) for(ll i=b-1; i>=a; i--) #define rvp4(i,a,b,c) for(ll i=b-1; i>=a; i-=c) #define rvp(...) overload4(__VA_ARGS__,rvp4,rvp3,rvp2,rvp1)(__VA_ARGS__) #define all1(v) v.begin(),v.end() #define all2(v,a) v.begin(),v.begin()+a #define all3(v,a,b) v.begin()+a,v.begin()+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(v) v.rbegin(),v.rend() #define rall2(v,a) v.rbegin(),v.rbegin()+a #define rall3(v,a,b) v.rbegin()+a,v.rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define each1(elem,v) for(auto &elem: v) #define each2(x,y,v) for(auto &[x,y]: v) #define each3(x,y,z,v) for(auto &[x,y,z]: v) #define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__) #define sqrp1(n) for(ll i=0; i*i void scan(T& a) { cin >> a; } template void scan(P& p) { scan(p.first); scan(p.second); } template void scan(V& a) { for(auto &i: a) scan(i); } void in(){} template void in(Head& head, Tail&... tail) { scan(head); in(tail...); } template void print(const T& a) { cout << a; } template void print(const P& p) { print(p.first); cout<<" "; print(p.second); } template void print(const V& a) { if(!a.empty()){ print(a[0]); for(auto i=a.begin(); ++i!=a.end();){ cout<<" "; print(*i); } } } void out(){ cout<<"\n"; } template void out(const T& t){ print(t); cout<<"\n"; } template void out(const Head& head, const Tail&... tail) { print(head); cout<<" "; out(tail...); } template void vout(V& v) { FE(v,[](T x){out(x);}); } }; // IO using namespace IO; #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define UL(...) ul __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define VEC(type,name,size) V name(size); in(name) #define WEC(type,name,h,w) V> name(h,V(w)); in(name) #define Fix(x) cout< void rev(T& v){ reverse(all(v)); } template void Sort(T& v){ sort(all(v)); } template void Sortt(T& v){ sort(rall(v)); } template T Min(const T& v){ return *min_element(all(v)); } template T Max(const T& v){ return *max_element(all(v)); } template inline ll dst(T& v, I itr){ return distance(v.begin(),itr); } template T LB(const V& v, U x){ return dst(v,lower_bound(all(v),x)); } template T UB(const V& v, U x){ return dst(v,upper_bound(all(v),x)); } template bool BS(const V& v, U x){ return binary_search(all(v),x); } template bool All(T& v, bool fn){ return all_of(all(v),fn); } template bool Exist(T& v, bool fn){ return any_of(all(v),fn); } template ll Find(T& v, const U x){ return dst(v.begin(),find(all(v),x)); } template T Count(V& v, ll x) { Sort(v); return UB(v,x)-LB(v,x); } template ul cntif(T& v, bool fn){ return count_if(all(v),fn); } template void rpl(T& v, bool fn, U r){ replace_if(all(v),fn,r); } template V iot(T n, T init){ V a(n); iota(all(a),init); return a;} template void ers(T& v, U x){ v.erase(remove(all(v),x),v.end()); } template ul unq(T& v){ Sort(v); v.erase(unique(all(v)),v.end()); return v.size(); } template void cp(const V& v, V u){ copy(all(v),back_inserter(u)); } template void rtt(T& v, ul idx){ rotate(all(v,idx),v.end()); } template V psum(V& v) { V s(v.size()); partial_sum(all(v),s.begin()); rtt(s,v.size()); return s; } template V adf(V& v){ V res(v.size()-1); adjacent_difference(all(v),res.begin()); return res; } }; // zia qu namespace Lady_sANDy { ll Mod(ll x, ll m){ return (x+m)%m; } ul Pow(ul a, uint b) { ul res=1; while(b>0) { if(b&1) res*=a; a*=a; b>>=1; } return res; } ll Ceil(ld x, ll m){ return ceil(x/m); } ld Round(ld x, ll m, uint fx){ if(fx==0) return (ll)round(x/m); else { ul y=Pow(10,fx+1); return round((x*y)/m/y); } } template T IP(const V& v, const V& u, T init){ return inner_product(all(v),u.begin(),init); } ll popcnt(ll x){ return __builtin_popcountll(x); } string to_hex(ll x) { stringstream s; s<(x); return s.str(); } template constexpr auto symin(T... a){ return min(initializer_list>{a...}); } template constexpr auto symax(T... a){ return max(initializer_list>{a...}); } template T kymin(map m){ return m.begin()->first; } template T kymax(map m){ return m.rbegin()->first; } template T stmin(set s){ return *s.begin(); } template T stmax(set s){ return *s.rbegin(); } }; // Lady s&y #define debug(...) { print(#__VA_ARGS__); print(": "); out(__VA_ARGS__); } #define elif else if #define scp(a,x,b) a<=x&&x<=b #define each_idx(el,v) &el-&v[0] //#define Mid(a,b) midpoint(a,b) #define mp make_pair #define mt make_tuple #define bit_check(bit,tar) (tar>>bit)&1 #define nxp(x) next_permutation(all(x)) #define prp(x) prev_permutation(all(x)) #define str_rpl(s,a,b) regex_replace(s,regex(a),b) #define ast(bool) assert(bool) namespace Heileden { /* BFS Sample template inline void bfs(V>& g, T start, vb& visited) { queue que; que.emplace(start); visited[start]=1; while(!que.empty()) { T v=que.front(); que.pop(); each(nv,g[v]) { if(!visited[nv]) { visited[nv]=1; que.emplace(nv); } } } }//*/ /* DFS Sample template inline void dfs(V>& g, T v, vb& visited) { visited[v]=1; each(nv,g[v]) if(!visited[nv]) dfs(g,nv,visited); }//*/ /* Permutation Sample template inline void nPr(V& v) { Sort(v); do {out(v);} while(nxp(v)); }//*/ // divisor template inline V divisor(T n) { V div; sqrp(i,1,n+1) { if(n%i==0) { div.emplace_back(i); if(i*i!=n) div.emplace_back(n/i); } } Sort(div); return div; } // prime judge inline bool is_prime(ul n) { sqrp(i,2,n+1) if(n%i==0) return 0; return 1; } // Siege of Eratosthenes inline vb SoE(ll n) { vb prime(n+1,1); if(n>=0) prime[0]=0; if(n>=1) prime[1]=0; sqrp(i,2,n+1) { if(!prime[i]) continue; rep(j,i*i,n+1,i) prime[j]=0; } return prime; } // prime factor template inline V> prmfct(T n) { V> res; rep(i,2,n+1) { if(n%i!=0) continue; T tmp=0; while(n%i==0) { tmp++; n/=i; } res.emplace_back(i,tmp); } if(n!=1) res.emplace_back(n,1); return res; } // square judge inline bool is_squere(ll n) { ll r=(ll)floor(sqrt((ld)n)); return r*r==n; } }; // Heileden // -------------------------------------------------------------------------------------------------------------- using namespace zia_qu; using namespace Lady_sANDy; using namespace Heileden; int main() { VvyLw::wa_haya_exe(); /*INT(t); while(t--)//*/ VvyLw::solve(); } // -------------------------------------------------------------------------------------------------------------- string ans(int n) { if(n==0) return "{}"; string res="{"; for(ll i=0; (1<