Score : $400$ points

Problem Statement

Given strings $S_1,S_2,S_3$ consisting of lowercase English letters, solve the alphametic $S_1+S_2=S_3$.

Formally, determine whether there is a triple of positive integers $N_1, N_2, N_3$ satisfying all of the three conditions below, and find one such triple if it exists. Here, $N'_1, N'_2, N'_3$ are strings representing $N_1, N_2, N_3$ (without leading zeros) in base ten, respectively.

• $N'_i$ and $S_i$ have the same number of characters.
• $N_1+N_2=N_3$.
• The $x$-th character of $S_i$ and the $y$-th character of $S_j$ is the same if and only if the $x$-th character of $N'_i$ and the $y$-th character of $N'_j$ are the same.

Constraints

• Each of $S_1$, $S_2$, $S_3$ is a string of length between $1$ and $10$ (inclusive) consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$S_1$

$S_2$

$S_3$

Output

If there is a triple of positive integers $N_1, N_2, N_3$ satisfying the conditions, print one such triple, using newline as a separator. Otherwise, print UNSOLVABLE instead.

a
b
c

1
2
3

Outputs such as $(N_1, N_2, N_3) = (4,5,9)$ will also be accepted, but $(1,1,2)$ will not since it violates the third condition (both a and b correspond to 1).

x
x
y

1
1
2

Outputs such as $(N_1, N_2, N_3) = (3,3,6)$ will also be accepted, but $(1,2,3)$ will not since it violates the third condition (both $1$ and $2$ correspond to x).

p
q
p

UNSOLVABLE

abcd
efgh
ijkl

UNSOLVABLE

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