#include using namespace std; #define rep(i, n) for(int i = 0; i < (n); ++i) #define per(i, n) for(int i = (n)-1; i >= 0; --i) #define eee(a) (cerr << (#a) << ": " << (a) << endl); #define ppp(a) (cout << (a) << endl); #define cop(a) for(auto x:(a)){cout << x << endl;} using ll = long long; using pint = pair; using pll = pair; using mint = map; int dx[4] = {1, 0, -1, 0}; int dy[4] = {0, 1, 0, -1}; constexpr char sp = ' '; constexpr char cmm = ','; constexpr int MOD = 1e9+7; constexpr int INF = 1e9; constexpr ll LINF = 1e18; constexpr double phi = (1+sqrt(5))/2; constexpr double pi = 3.14159265358979323846264338327950288; ll mod(ll a, ll b){return (a%b+b)%b;} ll gcd(ll a, ll b){return b?gcd(b,a%b):a;} ll lcm(ll a, ll b){return a*b/gcd(a,b);} inline void Yes(){puts("Yes");} inline void No(){puts("No");} inline void Judge(bool b){b?Yes():No();} inline void YES(){puts("YES");} inline void NO(){puts("NO");} inline void JUDGE(bool b){b?YES():NO();} inline ll powmod(ll b, ll e){ll r=1;while(e>0){if(e&1)r=(r%MOD)*(b%MOD)%MOD;b=(b%MOD)*(b%MOD)%MOD;e>>=1;}return r;} inline double distance(ll x1, ll y1, ll x2, ll y2){return sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));} inline double d2r(double d){return d*pi/180;} inline double r2d(double r){return r*180/pi;} templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream& operator<<(ostream& s, const pair& p) {return s << "(" << p.first << ", " << p.second << ")";} template ostream& operator<<(ostream& s, const vector& v) { s<<'[';for(size_t i=0;i