Description

Each problem setter has a Lawfulness index $L$ and a Goodness index $G$. For an idea, from the perspective of the statement, samples, or constraints, you must choose exactly one of the $6$ directions as the unique style of the problem corresponding to this idea, and you will move one step in the realm along the selected arrow direction:

Now you have a total of $n$ ideas. You know how your $L$ index and $G$ index change when you assign a certain style to each idea. Specifically, for the $i$-th idea, there are $12$ parameters $tl_{i,l},tl_{i,g},l_{i,l},l_{i,g},bl_{i,l},bl_{i,g},br_{i,l},br_{i,g},r_{i,l},r_{i,g},tr_{i,l},tr_{i,g}$:

If you choose “a concise statement”, then $L$ becomes $L+tl_{i,l}$, and $G$ becomes $G+tl_{i,g}$.

If you choose “ordinary and useless samples”, then $L$ becomes $L+l_{i,l}$, and $G$ becomes $G+l_{i,g}$.

If you choose “loose constraints”, then $L$ becomes $L+bl_{i,l}$, and $G$ becomes $G+bl_{i,g}$.

If you choose “a complex statement”, then $L$ becomes $L+br_{i,l}$, and $G$ becomes $G+br_{i,g}$.

If you choose “selfless gifted samples”, then $L$ becomes $L+r_{i,l}$, and $G$ becomes $G+r_{i,g}$.

If you choose “super super super loose constraints”, then $L$ becomes $L+tr_{i,l}$, and $G$ becomes $G+tr_{i,g}$.

All additions here are performed modulo $p$.

The requirements to enter the Chaotic Evil alignment are very strict: $L$ must be exactly equal to $L^*$ and $G$ must be exactly equal to $G^*$.

Initially, both your $L$ index and $G$ index are $0$. Determine whether there exists a way to assign styles such that after assigning styles to all $n$ ideas, you are still at the original position in the realm, and you can enter the Chaotic Evil alignment.

Input Format

The first line contains two positive integers $n,p$.

The next $n$ lines each contain $12$ non-negative integers $tl_{i,l},tl_{i,g},l_{i,l},l_{i,g},bl_{i,l},bl_{i,g},br_{i,l},br_{i,g},r_{i,l},r_{i,g},tr_{i,l},tr_{i,g}$. The order of the parameters is the same as in the problem description, and no additional checking is needed.

The last line contains two non-negative integers $L^*,G^*$.

Output Format

If possible, output one line Chaotic Evil.

If not possible, output one line Not a true problem setter.

3 10
3 5 1 4 9 3 0 0 0 0 0 0
0 0 0 0 0 0 3 5 1 4 9 3
3 5 1 4 9 3 3 5 1 4 9 3
3 2

Chaotic Evil

Hint

Sample Explanation

Assign the style “a concise statement” to the $1$-st idea. Then your Lawfulness index becomes $0+3=3$ and your Goodness index becomes $0+5=5$. You move one step to the upper-left.

Assign the style “loose constraints” to the $3$-rd idea. Then your Lawfulness index becomes $3+9=2$ and your Goodness index becomes $5+3=8$. You move one step to the lower-left.

Assign the style “selfless gifted samples” to the $2$-nd idea. Then your Lawfulness index becomes $2+1=3$ and your Goodness index becomes $8+4=2$. You move one step to the right. Now you are back at the origin, and your Lawfulness index is $3$ and your Goodness index is $2$. Therefore, you can enter the Chaotic Evil alignment.

Constraints

It is guaranteed that $1 \le n \le 100$ and $1 \le p \le 100$.

It is guaranteed that all other input data are between $0$ and $p-1$.

Source

From the 2021 Tsinghua University Student Programming Contest and Collegiate Invitational (THUPC2021).

Resources such as editorials can be found at https://github.com/yylidiw/thupc_1/tree/master.

Translated by ChatGPT 5