After being rejected by his AI girlfriend, Dragon needed a new talent to impress his crush.
In order to seek for love, Dragon decides to take on a new hobby: Ballet!

He has practiced a set of $N$ consecutive dance moves which can be represented on a 2-Dimensional coordinate plane.
The dance starts on $(S_x$, $S_y)$ and ends on $(E_x$, $E_y)$.
The $i$-th dance move $(0\leq i < N)$ can be viewed as moving $2^i$ times in the same direction.
He is able to move vertically, horizontally and diagonally or not move.

• If he moves vertically, he moves from $(x, y)$ to $(x, y\pm2^i)$.
• If he moves horizontally, he moves from $(x, y)$ to $(x\pm2^i, y)$.
• If he moves diagonally, he moves from $(x, y)$ to $(x\pm2^i, y\pm2^i)$.
• If he does not move, he remains at $(x, y)$.

He has marked the set of dance moves with a string of lowercase letters $S$ of length $N$.
However, he has already forgotten what direction each letter represents. All he knows is that all occurences of the same letter represent the same direction.
Can you help Dragon find a valid configuration of each letter or tell him that no such configuration exists?

Input

The first line contains 5 integers: $N, S_x, S_y, E_x, E_y$.
The second line consists of a string $S$ of length $N$.

Output

On the first line, output a valid configuration if it exists or -1 if there is not.
If a valid configuration exists, output $N$ pairs of characters consisting of +, - or / only.
The $i$-th pair represents the direction of the $i$-th dance move.

• /+ represents an upward move.
• /- represents a downward move.
• +/ represents a rightward move.
• -/ represents a leftward move.
• ++ represents an up-right move.
• -+ represents an up-left move.
• +- represents a down-right move.
• -- represents a down-left move.
• // represents not moving.

If there exists multiple configurations, you may output any of them.

Constraints

For all subtasks:

• $1 \leq N \leq 60$
• $1 \leq S_x, S_y, E_x, E_y \leq 2^{60}$
• $S$ consists of lowercase letters only.

Subtask 1 (10%): $N \leq 26$, $S[i] \neq S[j], 0 \leq i < j < N$
Subtask 2 (15%): $2^i = |S_x-E_x|, 2^j = |S_y-E_y|$ for some $i, j$
Subtask 3 (15%): $S[i]$ is a character from a to n.
Subtask 4 (20%): $N \leq 20$
Subtask 5 (40%): No additional constraints