#include #include using namespace std; namespace my{ #define eb emplace_back #define done(...) return pp(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij-->0;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i=i##stop;i+=i##step) #define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a) #define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;if(s)r[2]*=-1;return r;} constexpr char newline=10; constexpr char space=32; templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; pair operator+(const pair&p)const{return{a+p.a,b+p.b};} friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;} friend ostream&operator<<(ostream&o,const pair&p){return o<ostream&operator<<(ostream&o,const multiset&s){fe(s,e)o<struct multiset:std::multiset{ multiset(const initializer_list&a={}){fe(a,e)this->emplace(e);} multiset(const vector&a){fe(a,e)this->emplace(e);} ll size()const{return std::multiset::size();} T back()const{assert(size());return*this->rbegin();} }; templatestruct set:multiset{ set(const initializer_list&a={}){fe(a,e)this->emplace(e);} set(const vector&a){fe(a,e)this->emplace(e);} templateauto emplace(A&&...a){ T x(std::forward(a)...); if(auto p=this->find(x);p!=this->end())return pair{p,0}; return pair{multiset::emplace(x),1}; } }; templateauto pack_kth(const auto&...a){return get(make_tuple(a...));} templateauto pack_slice(const auto&...a){return[&](index_sequence){return array{get(forward_as_tuple(a...))...};}(make_index_sequence{});} templateconcept vectorial=is_base_of_v,V>; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){fe(v,e)o<?newline:space);return o;} templatestruct vec; templatestruct tensor_helper{using type=vec::type>;}; templatestruct tensor_helper<0,T>{using type=T;}; templateusing tensor=typename tensor_helper::type; templatestruct vec:vector{ using vector::vector; vec(const vector&v){vector::operator=(v);} templaterequires(sizeof...(A)>=3)vec(A...a){const ll n=sizeof...(a)-1;auto t=pack_slice(a...);ll s[n];fo(i,n)s[i]=t[i];*this=make_vec(s,pack_kth(a...));} templatestatic auto make_vec(const ll(&s)[n],T x){if constexpr(i==n-1)return vec(s[i],x);else{auto X=make_vec(s,x);return vec(s[i],X);}} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator+=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]-=u[i];return v;} vec operator+(const vec&u)const{return vec{*this}+=u;} vec operator-(const vec&u)const{return vec{*this}-=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;} vec&operator%=(auto M){vec&v=*this;fe(v,e)e%=M;return v;} vec operator%(auto M)const{return vec{*this}%=M;} ll size()const{return vector::size();} auto decode(const string&b="a")const{conditional_t,vec,string>r;fe(*this,e)if constexpr(vectorial)r.eb(e.decode(b));else r+=b.size()==1?e+b[0]:b[e];return r;} }; templaterequires(sizeof...(A)>=2)vec(A...a)->vec(declval>()))>>>; vec(ll)->vec; void lin(auto&...a){(cin>>...>>a);} auto sinen(const string&b="a"){string s;lin(s);vecr;fe(s,e)r.eb(b.size()==1?e-b[0]:b.find_first_of(e));return r;} auto sinen(ll n,const string&b="a"){vec>r;fo(n)r.eb(sinen(b));return r;} void pp(auto&&...a){ll n=sizeof...(a);((cout<0,space)),...);cout<>ng; fo(i,N)ng.emplace(s[i]); vec cu(N); while(1){ if(!ng.count(cu))done(cu.decode()); ll r=1; of(j,N){ if(r==1){ if(cu[j])r=1; else r=0; cu[j]^=1; } } } }}