#include typedef long long ll; using namespace std; const int INF = 1e9; const int MOD = 1e9+7; const ll LINF = 1e18; #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define REP(i,n) for(int i=0;i<(n);++i) #define REPR(i,n) for(int i=n;i>=0;i--) #define ALL(v) (v.begin(),v.end()) #define COUT(x) cout<<(x)<<'\n' template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } bool prime(ll n){ ll n_root = sqrt(n); if(n==1)return false; else if(n==2)return true; else if (n%2==0)return false; for(int i=3;i> n; bool flag = false; for(int i=2;i