You have stumbled upon a village with n people.

In this village, at most k of the people are "imposters", while the rest are not

You would like to determine who is not an imposter in this village. To do so,
you ask each villager to submit a list of some villagers who are not imposters.

Non-imposters will only submit lists that contain other non-imposter names, while
there is no such restriction for imposters.

Given the lists of each villager, determine whether they could possibly be an imposter, or are definitely not an imposter.


Bounds:
1 <= k <= n <= 500

input format:
n k
s_1 x_{1,1} x_{1,2} ... x_{1,s_1}
s_2 x_{2,1} x_{2,2} ... x_{2,s_2}
...
s_n x_{n,1} x_{n,2} ... x_{n,s_n}

s_i denotes the number of people in the i-th person's list.
x_{i,j} denotes the j-th person on the i-th person's list
It is possible a person appears in their own list.
It is guaranteed that x_{i,1} x_{i,2} ... x_{i,s_i} are all distinct.

output:

Print a string with n characters
The i-th character is 'X' if the villager could possibly be an imposter, and 'O' if they are definitely not an imposter.
