#define MD 998244353
int p[7d5],q[1d7]{},r[1d7],s[1d7];
ll np=Prime(1d7,p);
rep(i,np){
	q[p[i]]=1;
}
int a=0,b=0;
rep(i,1d7){
	r[i]=a+=q[i];
	s[i]=b;
	b+=q[i]*q[i^2];
	if(i>(i^2)){
		s[i]=b;
	}
}
ll@t;
rep(t){
	ll@n,@m;
	if(n==1){
		wt(r[m]);
	}else{
		--n;
		n<<=2;
		ll a=1,b=0,c=0,d=1;
		rep(30){
			ll e=a*a+b*c;
			ll f=b*(a+d);
			ll g=c*(a+d);
			ll h=d*d+b*c;
			if((int)n<0){
				a=f%MD*s[m];
				b=e+f;
				c=h%MD*s[m];
				d=g+h;
			}else{
				a=e;
				b=f;
				c=g;
				d=h;
			}
			a%=MD;
			b%=MD;
			c%=MD;
			d%=MD;
			n<<=1;
		}
		wt((a+c+s[m]*(b+d))%MD);
	}
}