This is a non-standard but still positional **numeral system**. It's feature is that digits can have one of values `-1`

, `0`

and `1`

.
Nevertheless its base is still `3`

(because there are three possible values). Since it is not convenient to write `-1`

as a digit
we'll use letter `Z`

further for this purpose. If you think it is quite strange system - look at the picture - here is one of the
computers utilizing it.

So here are few first numbers written in balanced ternary:

```
0 0
1 1
2 1Z
3 10
4 11
5 1ZZ
6 1Z0
7 1Z1
8 10Z
9 100
```

This system allows to write negative values without leading minus sign: you can simply invert digits in any positive number

```
-1 Z
-2 Z1
-3 Z0
-4 ZZ
-5 Z11
```

Note that negative number starts with `Z`

and positive with `1`

.

It is easy to convert represent number in **balanced ternary** via temporary representing it as normal ternary. When value is
in standard ternary, its digits are either `0`

or `1`

or `2`

. Iterating from the lowest digit we can safely skip any `0`

s and `1`

s,
however `2`

should be turned into `Z`

with adding `1`

to the next digit. Digits `3`

should be turned into `0`

on the same terms -
such digits are not present in the number initially but they can be encountered after increasing some `2`

s.

**Example:** let us convert `64`

to balanced ternary. At first we use normal ternary to rewrite the number:

$$ 64 = 02201_{3} $$

Let us process it from the least significant (rightmost) digit:

`1`

is skipped as is,`0`

at the next position too;`2`

is turned into`Z`

increasing the following digit, so we get`03Z01`

(temporarily);`3`

is turned into`0`

increasing the following digit (which, luckily, was`0`

).

So the result is `10Z01`

.