Field Day

문제

Each of Farmer John's $NN$ barns ($2\le N\le {10}^{5}2\backslash le\; N\backslash le\; 10^5$) has selected a team of $CC$ cows ($1\le C\le 181\backslash le\; C\backslash le\; 18$) to participate in field day. The breed of every cow is either a Guernsey or a Holstein.

The difference between two teams is defined to be the number of positions $ii$ ($1\le i\le C1\; \backslash leq\; i\; \backslash leq\; C$) at which the breeds of the cows in the $ii$th positions differ. For every team $tt$ from $1\dots N1\; \backslash ldots\; N$, please compute the maximum difference between team $tt$ and any other team.

입력

The first line contains $CC$ and $NN$.

The next $NN$ lines each contain a string of length $CC$ of Gs and Hs. Each line corresponds to a team.

출력

For each team, print the maximum difference.

힌트

The first and third teams differ by $55$. The second and third teams differ by $33$.

5 3
GHGGH
GHHHH
HGHHG

5
3
5