Monika loves to play with strings very much. One day she found a very large string S. Now she want to play with this string along with Rahul. She asked Rahul a simple problem to find the longest good substring of S such that number of consonants in that substring is no more than thrice the number of vowels. That is, the substring with v vowels and c consonants is good if and only if c ≤ 3v.

He should also find the number of the longest good substrings of the string S.

Input:
The first line of the input contains T, the number of test cases. Then follows T lines.
Each line contains a non-empty string S consisting of no more than 10^5 uppercase and lowercase letters. We shall consider letters "a", "e", "i", "o", "u" and their uppercase variants as vowels.

Output:
For each test case print on a single line two numbers separated by a space: the maximum length of a good substring and the number of good substrings with this length. If no good substring exists, print "-1" (without quotes).

Two substrings are considered different if their positions of occurrence are different. So if some string occurs more than once, then it should be counted more than once.

Constraints:
1 <= T <= 500
1 <= length of S <= 10^5

Problem Setter:

Akash Rakshit