There are $n$ friends and $n$ houses in Chess City, both numbered from $1$ to $n$, where friend $i$ lives in house~$i$. The houses are connected by $m$ bidirectional roads, forming a connected network.

Chess City also has $n$ virtual chess clubs, numbered from $1$ to $n$. Each friend must choose exactly one club to join. These choices do not need to be distinct, so some clubs might not have any members.

When friend $i$ hosts a chess party, it is attended by every friend who belongs to the same club as friend~$i$ and lives in a house directly connected to house $i$ by a road. The party is considered \textit{successful} if the total number of attendees, including friend $i$, is even; in this case, they can all play chess simultaneously.

Choose a club for each friend so that every friend's party is successful, or report that it is impossible.
