- 61

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

Although ternary computing has fallen out of favor these last 40 years or more, there is reason to think that it may be an important part of the future. Whereas each digit in a binary system has two possible states, ternary digits have three possible states. In the Balanced Ternary system, each digit represents either -1, 0, or +1.In binary, each digit is worth its face value (1 or 0) multiplied by a power of two determined by its position:

**Binary**

┌──────> 1 * (2^3) = 8

│┌─────> 1 * (2^2) = 4

││┌────> 0 * (2^1) = 0

│││┌───> 1 * (2^0) = 1

1101 = 13

In Balanced Ternary, the system is similar except each value (-1, 0, or +1) is multiplied by a power of

**3**determined by its position. "1" and "0" represent themselves and "T" represents -1 (it sort of looks like "-1", right?):

**Balanced Ternary**

┌───────> +1 * (3^4) = 81

│┌──────> -1 * (3^3) = -27

││┌─────> 0 * (3^2) = 0

│││┌────> +1 * (3^1) = 3

││││┌───> -1 * (3^0) = -1

1T01T = 56

In order to be able to use Balanced Ternary, we need to be able to do some rudimentary operations. You must develop an application that can evaluate expressions using five binary operators: left shift, right shift, addition, subtraction, and multiplication. The shift operators do not wrap. Some examples:

**Examples**

1T0 >> 1 = 1T

1T0 >> 1T = 1

1T0 << 1 = 1T00

1T0 + 1 = 1T1

1T1 + 1 = 10T

1T0 - 1 = 1TT

1T * 1T = 11

Note: You may want to complete the easier related puzzle first: https://www.codingame.com/training/easy/balanced-ternary-computer-encode

Input

**Line 1:**The first operand,

`lhs`.

**Line 2:**The operator,

`op`.

**Line 3:**The second operand,

`rhs`.

Output

A single line containing the evaluation of the input expression in Balanced Ternary,

`ret`.Constraints

**In Decimal:**

-3280 <=

`lhs`<= 3280

-3280 <=

`rhs`<= 3280

-3280 <=

`ret`<= 3280

**In Balanced Ternary:**

TTTTTTTT <=

`lhs`<= 11111111

TTTTTTTT <=

`rhs`<= 11111111

TTTTTTTT <=

`ret`<= 11111111

`op`is one of

Example

Input

1T1 + 11

Output

11T

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