inline int scan( ) {

int n=0;

int ch=getchar_unlocked();

while( ch <48 )ch=getchar_unlocked();

while( ch >47 )

n = (n<<3)+(n<<1) + ch-'0', ch=getchar_unlocked();

return n;

}

n = (n<<3)+(n<<1) + ch-'0', ch=getchar_unlocked();