Burned Calendar

Time Limit: 1 Second Memory Limit: 32768 KB

A year calendar is printed using the monospace font according to the following rules:

1) All spaces on the printed calendar are represented by the dot character (ASCII 46).

2) Every month occupies a rectangle of 17 by 8 characters, with the name of the month written in all capital letters starting from the 2nd character of the first line.

3) All days of the months are printed in 4, 5, or 6 columns 2 characters wide and 7 characters high, with one space between the columns. The first day of the week is Monday.

a. Months of the year are arranged in the three rows separated by horizontal and vertical lines of spaces. Each row contains four months. The calendar margins are of 1 space from all sides. Therefore, the whole calendar has size of 73 by 28 characters.

Note that January 1st, 1900 was Monday. Also note that a leap year number is divisible by 4 and not divisible by 100, or divisible by 400. For example, a part of the printed calendar from October to December 2002 may look like this:

.OCTOBER...........NOVEMBER..........DECEMBER.........
....7.14.21.28........4.11.18.25........2..9.16.23.30.
.1..8.15.22.29........5.12.19.26........3.10.17.24.31.
.2..9.16.23.30........6.13.20.27........4.11.18.25....
.3.10.17.24.31........7.14.21.28........5.12.19.26....
.4.11.18.25........1..8.15.22.29........6.13.20.27....
.5.12.19.26........2..9.16.23.30........7.14.21.28....
.6.13.20.27........3.10.17.24........1..8.15.22.29....
......................................................

A calendar was printed and then burned, with only a small rectangular piece left. Your program must determine to which of years from 1900 to 2100 this piece could belong.

Input

The first line of the input contains integer numbers N and M (2 <= N, M <= 10), separated by spaces - the size of the piece. The following M lines contain N characters each - the piece of calendar.

Output

Output must contain an ordered list of year numbers, one year per line. If given piece could not belong to any calendar, output must contain a single integer 0 (zero).

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

Sample Input

2
 
4 4
1..8
....
JUNE
1..8

3 2
1.7
...

Sample Output

Submit

Source: Northeastern Europe 2002, Far-Eastern Subregion