template <class Ran, class X>
bool binary_search(Ran begin, Ran end, const X& x)
{
	while (begin < end) {
		// find the midpoint of the range
		Ran mid = begin + (end - begin) / 2;

		// see which part of the range contains `x';
		// keep looking only in that part
		if (x < *mid)
			end = mid;
		else if (*mid < x)
			begin = mid + 1;
		// if we got here, then `*mid == x' so we're done
		else return true;
	}
	return false;
}