bee 1942 - Lottery

The BWS lottery is done annually. In it N people bet by choosing K numbers each. Formally, we can say that B_ij is the j-th amount wagered by the i-th person. So the organizers choose positive integers K. The chosen numbers are called W₁, W₂, ..., W_K.

Winners are calculated as follows:

A non-empty subset of N participants is randomly chosen, in other words, some participants are chosen by pure luck.
For each person in this subset S₁ value is calculated, which is the sum of all first numbers bet by them, that is, the sum of B_i1, where i would be the index of the chosen person. Likewise S₂, ..., S_K values are calculated.
It is made a parity test between Sj and Wj, in other words, it is tested whether the parities (if the number is odd or even) match between S₁ and W₁, W₂ and S₂, and so on until W_K and S_K.
If all parities matches, then this group of persons is declared the winner!

The organizers want to know: can you choose the numbers W₁, W₂, ..., W_K so that there is no winner subset of participants?

Input

The first line contains the numbers N (1 ≤ N ≤ 10⁴) and K (3 ≤ K ≤ 50), representing the number of participants and the amount of numbers bet per person respectively. People bet on integers greater than 1 and smaller than 50, inclusive. Each of the following N lines contains K numbers, representing the bets of each person, one per line.

Output

Print 'S' if possible or 'N' otherwise.

Input Samples	Output Samples
2 3 1 2 3 5 6 7	S

Input Samples

Output Samples

2 3

1 2 3

5 6 7

3 3 3 2 1 6 5 4 4 4 4	S

3 3

3 2 1

6 5 4

4 4 4

4 3 9 4 7 4 4 4 2 7 2 2 2 1	N

4 3

9 4 7

4 4 4

2 7 2

2 2 1