#include using namespace std; const long long MOD=1000000007; // const long long MOD=998244353; #define LOCAL #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(),(x).end() const int INF=1e9; const long long IINF=1e18; const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1}; const char dir[4]={'D','R','U','L'}; template istream &operator>>(istream &is,vector &v){ for (T &x:v) is >> x; return is; } template ostream &operator<<(ostream &os,const vector &v){ for (int i=0;i ostream &operator<<(ostream &os,const pair &p){ os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream&operator<<(ostream &os,const tuple &t){ os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')'; return os; } template ostream&operator<<(ostream &os,const tuple &t){ os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')'; return os; } template ostream &operator<<(ostream &os,const map &m){ os << '{'; for (auto itr=m.begin();itr!=m.end();){ os << '(' << itr->first << ',' << itr->second << ')'; if (++itr!=m.end()) os << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os,const unordered_map &m){ os << '{'; for (auto itr=m.begin();itr!=m.end();){ os << '(' << itr->first << ',' << itr->second << ')'; if (++itr!=m.end()) os << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os,const set &s){ os << '{'; for (auto itr=s.begin();itr!=s.end();){ os << *itr; if (++itr!=s.end()) os << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os,const multiset &s){ os << '{'; for (auto itr=s.begin();itr!=s.end();){ os << *itr; if (++itr!=s.end()) os << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os,const unordered_set &s){ os << '{'; for (auto itr=s.begin();itr!=s.end();){ os << *itr; if (++itr!=s.end()) os << ','; } os << '}'; return os; } template ostream &operator<<(ostream &os,const deque &v){ for (int i=0;i void debug_out(Head&& head,Tail&&... tail){ cerr << head; if (sizeof...(Tail)>0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) cerr << " ";\ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\ cerr << " ";\ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x,T y){return y!=0?gcd(y,x%y):x;} template T lcm(T x,T y){return x/gcd(x,y)*y;} template inline bool chmin(T1 &a,T2 b){ if (a>b){a=b; return true;} return false; } template inline bool chmax(T1 &a,T2 b){ if (a> S; for (int i=0;i