Growth wants to know whether the people who join come back. A user's cohort is the first day they were active; retention asks how many of that cohort returned on a particular later day.

Input

A user can appear many times on one day, and a day with no activity has no row.

Output

One row per cohort that exists in the data, with the columns:

• cohort_date — 'YYYY-MM-DD', the cohort's first active day
• cohort_size — distinct users whose first active day is that date
• day_1_retained — how many of them were active again exactly one day later
• day_7_retained — how many were active exactly seven days later

Example

Constraints

• Exactly one day and exactly seven days, not "within". A user who returns on day 8 is retained on neither, and a user who returns on day 1 is not thereby retained on day 7.
• A user belongs to one cohort — their own first day — regardless of how long they stay around.
• Several rows for one user on one day are one active user.
• Row order is not graded. Column names and their order are.