Words with the same letters

Problem

A word game puts two words in the same group when one is a rearrangement of the other. Print the number of groups and the size of the largest group.

Example 1

Input

6
listen
silent
enlist
google
cat
act

Output

3 3

Groups of three, one and two.

Example 2

Input

2
ab
cd

Output

2 1

Try the problem first. Open one hint at a time.

Hint 1

Two words are in the same group when their sorted letters are equal.

Hint 2

Use the sorted letters as a dictionary key and count how many words share each key.

Write your Python code, run it on the examples and submit it to hidden tests.