#include #include // url #define rep(i,a,b) for(int i=a;i=a;i--) #define all(x) (x).begin(),(x).end() #define pb(x) push_back(x); templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b; // using mint = static_modint<1000000007>; const ll mod=998244353; //const ll mod=1e9+7; int dx[4]={1,0,-1,0}; int dy[4]={0,1,0,-1}; const string zton="0123456789"; const string atoz="abcdefghijklmnopqrstuvwxyz"; const string ATOZ="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const ll inf=(1ll<<60); // const int inf=(1<<30); ll dist(ll x1,ll x2,ll y1,ll y2){ ll res=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2); // res=sqrt(abs(res)); return res; } lld arg(lld x,lld y){ const lld eps=1e-8; lld res=0; if(abs(x)+abs(y)<=eps)return 0.0; else if(abs(x)<=eps){ if(y>=0.0)return (M_PI/2); else return (M_PI/2+M_PI); } else if(abs(y)<=eps){ if(x>=0.0)return 0.0; else return M_PI; } res=atan2(abs(y),abs(x)); if(x<=0&&y>=0)res=(M_PI-res); else if(x<=0&&y<=0)res+=(M_PI); else if(x>=0&&y<=0)res=(M_PI*2-res); return res; } ll gcd(ll a,ll b){ if(a==0||b==0)return a+b; ll r; r=a%b; if(r==0){ return b; } else{ return gcd(b,r); } } typedef pair P; // ll sqrtl(ll x2){ // ll ok=0; // ll ng=1e9+1; // while(ok+1!=ng){ // ll mid=(ok+ng)/2; // if(mid*mid<=x2)ok=mid; // else ng=mid; // } // return ok; // } const ll l=1e9; int main(void){ ios::sync_with_stdio(false); cin.tie(nullptr); // for(ll y1=l;y1>=2;y1--){ // ll x12=y1*y1-1; // if(x12%3!=0)continue; // x12/=3; // ll x1=sqrtl(x12); // if(x1*x1==x12){ // cout<