I am having problem writing a custom comparator for priority queue in C++. The elements' type in the queue is pair<long long,pair<long long, long long>> I want the queue to rank the elements with the smallestfirst element first, and if there is a tie, rank the elements with the smallest second.first element first. If there's a tie again, rank the element with the smallest second.second element first. So I have the following comparator and declaration:

class cmp {
public:
	bool operator()(pair<long long, pair<long long, long long>> A, pair<long long, pair<long long, long long>> B) {
		if (A.first > B.first) {
			return true;
		}
		if (A.first < B.first) {
			return false;
		}
		if (A.first == B.first) {
			if (A.second.first > B.second.first) {
				return true;
			}
			if (A.second.first < B.second.first) {
				return false;
			}
			if (A.second.second > B.second.second) {
				return false;
			}
			return true;
		}
	}
};

int main()
{
	priority_queue<pair<long long, pair<long long, long long>>,vector<pair<long long,pair<long long,long long>>>,cmp> q;
	q.push(make_pair(0, make_pair(1, 1)));//first element
	q.push(make_pair(9, make_pair(1, 1)));//second element
	q.push(make_pair(0, make_pair(1, 2)));//third element
}

However, when I push the three elements shown in the code, the queue does not give me the correct ranking of first, third, and second. I am sure I made some mistake but I couldn't find it. Please help me. Thank you!