You are given a list of people who are attending ACM-ICPC World Finals. Each of them are either well versed in a topic or they are not. Find out the maximum number of topics a 2-person team can know. And also find out how many teams can know that maximum number of topics.
Note Suppose a, b, and c are three different people, then (a,b) and (b,c) are counted as two different teams.
Input Format
The first line contains two integers, and , separated by a single space, where represents the number of people, and represents the number of topics. lines follow. Each line contains a binary string of length . If the th line's th character is , then the th person knows the th topic; otherwise, he doesn't know the topic.
Constraints