Problem Statement

There is a sequence $A=(A_1, A_2, \cdots, A_N)$ of length $N$.

Now, Shiki is going to settle the black and white of the sequence $A$.

Here, to settle the black and white of a sequence means the following operation.

• Assign white or black to each element of the sequence, so that the following condition is satisfied.
  • Let $W, B$ be the total bitwise OR of the elements assigned white and black, respectively ($W=0$ if all elements are assigned black, and similarly $B=0$ if all are assigned white). Then $W\mathbin{\&}B=0$.

Here, $X\mathbin{\&}Y$ denotes the bitwise AND of $X$ and $Y$.

Find the maximum possible value of $W\times B$ when Shiki settles the black and white of the sequence $A$. Also, find one color assignment that achieves the maximum value.

Input

$N$
$A_1\ A_2\ \cdots\ A_N$

• $1\leq N\leq 100$
• $0\leq A_i\leq 4000$
• All inputs are integers.

Output

Let $M$ be the maximum possible value of $W\times B$. For a color assignment achieving it, let $S$ be the string such that $S_i=$W if the color assigned to $A_i$ is white and $S_i=$B if it is black. Output them in the following format.

If there are multiple possible $S$, you may output any of them.

$M$
$S$

Print a newline at the end.

Sample

3
4 2 2

8
WBB

3
60 3 64

4032
BBW