emails has columns email_id, to_user and day. activity has columns user_id, session_id and day.

For every (user, day) pair appearing in either table, count the emails that user received and the distinct sessions they opened, treating an absent side as 0. Return the Pearson correlation between those two counts as a float.

A user-day present in one table and missing from the other is a real zero, not a row to drop, and dropping them would change the answer.

Input

emails =
   email_id to_user  day
0         1      u1    1
1         2      u1    1
2         3      u2    1
3         4      u3    2
activity =
  user_id  session_id  day
0      u1          10    1
1      u1          11    1
2      u2          12    1
3      u2          12    1
4      u4          13    1

Output

0.5