FitTrail, a fitness-tracking app, records an entry every time a user logs a workout, but it only stores the date — if a user works out twice on the same day, two entries with that same date can still appear. Product analytics wants an early-retention signal: among all users, what fraction kept training on the very next calendar day after their first-ever logged workout?

You are given every logged entry. For each user, find the earliest date on which they logged a workout — call it their kickoff date. A user counts as retained if any of their entries show a workout on the calendar day immediately following their kickoff date (a later date does not count, only exactly the next day). Compute the fraction of ALL users, retained or not, that are retained, rounded to exactly two decimal places.

Input format

• Line 1: a single integer n — the number of workout entries.
• Each of the next n lines contains two space-separated tokens: an integer user_id and a date date in "YYYY-MM-DD" format, meaning that user logged a workout on that date. The same (user_id, date) pair may appear more than once, and entries are given in no particular order.

Output format

Print a single number: the retention fraction, rounded to exactly 2 decimal places (for example 0.50, 1.00, or 0.33), with the trailing zero(s) always shown.

Constraints

• 1 <= n <= 2 * 10^5
• 1 <= user_id <= 10^9
• Every date is a valid calendar date between 2000-01-01 and 2099-12-31 inclusive.

3
1 2024-01-01
1 2024-01-02
2 2024-01-05

0.50

6
1 2024-03-10
1 2024-03-11
2 2024-03-10
2 2024-03-10
3 2024-05-01
3 2024-05-03

0.33