Problem Statement

There are $N$ people numbered $1,2,\ldots,N$. For $i\neq j$, the intimacy between persons $i$ and $j$ is $A_{i,j}$.

For each of the $N$ people, assign room $X$ or room $Y$. Each of the $N$ people moves to their assigned room. It is acceptable if there is an empty room.

Person $i$ is in a good state if the following is satisfied:

(Sum of intimacy with person $i$ of all people in the same room as person $i$) $\geq$ (Sum of intimacy with person $i$ of all people in a different room from person $i$).

Output one assignment of rooms such that all $N$ people are in a good state.

It can be proved that such an assignment always exists.

Constraints

• $2 \leq N \leq 50$
• $-50 \leq A_{i,j} \leq 50$
• $A_{i,j} = A_{j,i}$
• $A_{i,i}=0$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_{1,1} A_{1,2} \cdots A_{1,N}
A_{2,1} A_{2,2} \cdots A_{2,N}
\vdots
A_{N,1} A_{N,2} \cdots A_{N,N}

Output

Output one assignment that satisfies the condition. If there are multiple solutions, you may output any of them. Represent the assignment by a string $S$ of length $N$. If person $i$ is assigned to room $X$, the $i$-th character of $S$ should be X; if assigned to room $Y$, the $i$-th character of $S$ should be Y.