Description

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

• All spaces on the printed calendar are represented by dots (ASCII 46).

Note that January 1st, 1900 was Monday. Also note that the year is a leap year if its 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 looks 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....
......................................................

The 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 file contains integer numbers N and M - the sizes of the piece, separated by spaces. The following M lines contain N characters each - the piece of calendar. 2 <= N, M <= 10

Output

Output file 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).

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

1903
1914
1925
1931
1942
1953
1959
1970
1981
1987
1998
2009
2015
2026
2037
2043
2054
2065
2071
2082
2093
2099

Source

Northeastern Europe 2002, Far-Eastern Subregion