Loteria

The BWS Loteria draw is held once a year. $N$ people enter it, and each of them picks $K$ numbers. Write $B_{i,j}$ for the $j$-th number picked by the $i$-th person. The organizers then pick $K$ positive integers of their own, called $W_1, W_2, \dots, W_K$.

The winners are decided like this.

• A non-empty subset of the $N$ entrants is drawn at random.
• Add up the first number picked by every person in that subset and call the total $S_1$. That is, $S_1$ is the sum of $B_{i,1}$ over the indices $i$ in the subset. Compute $S_2, \dots, S_K$ the same way.
• For every $j$, check whether $W_j$ and $S_j$ have the same parity, meaning both are even or both are odd.
• If the parities agree for every $j$, that set of people wins.

The organizers want to know whether they can pick $W_1, W_2, \dots, W_K$ so that no subset of the entrants wins.

The first line contains the number of entrants $N$ and the count of numbers each person picks, $K$. ($1 \le N \le 10^4$, $3 \le K \le 50$)

Each of the next $N$ lines contains the $K$ numbers picked by one person. Every picked number is an integer between $1$ and $50$, inclusive.

Print S if the organizers can pick $W_1, W_2, \dots, W_K$ so that no subset wins, and N otherwise.