# Problem B - Unattainable Numbers

In the fall of 1989 Paul Loomis was a sophomore at Wabash
College. During an uninspiring lecture, he tried to find an
interesting number sequence. And he found something he liked! Imagine
the following function:

f(n) = n + (the product of the nonzero digits of n)

If we begin with the number 1, by iterating f, we obtain the
following sequence:

1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, 104, 108, (...)

For example, from 22, we get `f(22) = 22 + 2*2 = 22 + 4 =
26`. And then, `f(26) = 26 + 2*6 = 26 + 12 = 38`. When he
have zeros, we ignore them in the product, as we said before. For
example, `f(102) = 102 + 1*2 = 104`. If we start with another
number, we have another sequence that eventually hits a number in the
first sequence we gave. For example, if we start with 5 or 19:

5, 10, 11, 12, 14, 18, 26, (...)
19, 28, 44, 60, 66, 102, (...)

However, some numbers are "unattainable" in the sense that for
obtaining them using the function described before, we must use them
as the starting number. More formally, a number `n` is
unattainable if there exists no `m > 0`, such that `f(m) =
n` (the same as saying there exists no `m > 0` such that `m
+ (the product of the nonzero digits of m) = n`). For example, 1,
5 and 19 are unattainable numbers.

## The Problem

For a given number, you have to discover if it is an unattainable one.

## Input

In the first line of input comes an integer number **C**,
indicating the quantity of numbers to evaluate (1 ≤ C ≤ 10
000).

Then follow exactly **C** lines, each one with one integer **N**,
indicating the numbers you should evaluate (1 ≤ N ≤ 1 000 000).

## Output

The output has exactly **C** lines, each one indicating if the respective number is unattainable, in the following format:

N is unattainable

or
N is not unattainable

See the sample input and output for a concrete example.

## Sample Input

7
1
74
11
5
19
63
66

## Sample Output

1 is unattainable
74 is not unattainable
11 is not unattainable
5 is unattainable
19 is unattainable
63 is unattainable
66 is not unattainable

**TIUP & CPUP 2007**

Universidade do Porto

*(30 de Maio de 2007)*