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


Output Format

On the first line, print the maximum number of topics a 2-person team can know.
On the second line, print the number of 2-person teams that can know the maximum number of topics.

Sample Input

4 5
10101
11100
11010
00101
Sample Output

5
2
Explanation

(1, 3) and (3, 4) know all the 5 topics. So the maximal topics a 2-person team knows is 5, and only 2 teams can achieve this.