Rosita wrote in a notebook the dates (day and month) of $k$ consecutive days and stored this notebook in a box. After a few years, Rosita found her notebook, but sadly the months she wrote were unreadable. Rosita wants to know all possible months of the last date she wrote in the notebook.

A line with an integer $k$ $(1 \le k \le 300)$ denoting how many dates were written. Next line contains $k$ integer numbers: the days of every date in the same order they were written. These days are guaranteed to be from a valid sequence of consecutive dates.

Print the number of possible months of the last date Rosita wrote in her notebook. In the next lines print the possible months, one per line, in calendar order.

Input

10
1 2 3 4 5 6 7 8 9 10

Output

12
January
February
March
April
May
June
July
August
September
October
November
December

Input

2
31 1

Output

7
January
February
April
June
August
September
November

Input

11
20 21 22 23 24 25 26 27 28 29 1

Output

1
March