There are n students in a dormitory, each with a sleep start time (s) and a sleep end time (e) during a day. Each student requires a single mattress to sleep on. A mattress can be shared among several students during the day, but at a certain point in time a mattress can be occupied by at the most one student. Find the minimum number of mattresses m required in the dormitory such that all the students are accommodated. For such m, find the duration where all mattresses are being used.

Constraints
1 <= t <= 20

1 <= n <= 10^5

1 <= e - s (in seconds) <= 24 * 60 * 60

Time format is a 24 hour clock with start of the day as 00:00:00 and end as 24:00:00.

Input Format
The first line contains a single integer t, denoting the number of test cases.
The first line of each test case contains a single integer n denoting the number of students.
Following n lines contains the start s and end e for each student space separated.

Output Format
For each test case print the minimum number of mattresses m and for such m the total duration where all the m mattresses are being used separated by space.

Sample Input
4
8
18:30:00 21:30:00
07:00:00 23:00:00
14:30:00 22:00:00
01:30:00 11:30:00
07:30:00 13:00:00
22:30:00 23:30:00
17:30:00 18:00:00
01:00:00 02:30:00
4
01:00:00 02:00:00
03:00:00 04:00:00
04:00:00 12:00:00
15:00:00 24:00:00
5
13:00:00 24:00:00
00:00:00 08:00:00
14:00:00 24:00:00
08:00:00 14:00:00
00:00:00 13:00:00
1
20:30:00 21:00:00
Sample Output
3 07:30:00
1 19:00:00
2 24:00:00
1 00:30:00
Explanation
For the first case

8
18:30:00 21:30:00
07:00:00 23:00:00
14:30:00 22:00:00
01:30:00 11:30:00
07:30:00 13:00:00
22:30:00 23:30:00
17:30:00 18:00:00
01:00:00 02:30:00
3 mattresses are required. See diagram below

Usage of mattress 1 is shown in red, mattress 2 in green and mattress 3 in blue.

All the three mattresses are being used from 07:30:00 - 11:30:00, 17:30:00 - 18:00:00, 18:30:00 - 21:30:00 giving a total of
04:00:00 + 00:30:00 + 03:00:00 = 07:30:00.