struct Gray {

	Uint gray(const Uint n) {return n ^ (n >> 1);}

	Uint invgray(const Uint n) {
		Int ish=1;
		Uint ans=n,idiv;
		for (;;) {
			ans ^= (idiv=ans >> ish);
			if (idiv <= 1 || ish == 16) return ans;
			ish <<= 1;
		}
	}
};