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## Statement

## Goal

The quarternions belong to a number system that extends the complex numbers. A quarternion is defined by the sum of scalar multiples of the constantsMore information is available at http://mathworld.wolfram.com/Quaternion.html

Consider the following properties:

These properties also imply that:

The order of multiplication is important.

Your program must output the result of the product of a number of bracketed simplified quarternions.

**Pay attention to the formatting**

The coefficient is appended to the left of the constant.

If a coefficient is

If a coefficient or scalar term is

The terms must be displayed in order: a

**Example Multiplication**

(2i+2j)(j+1) = (2ij+2i+2j² +2j) = (2k+2i-2+2j) = (2i+2j+2k-2)

Input

**Line 1**:The expression

`expr`to evaluate. This will always be the product of simplified bracketed expressions.

Output

A single line containing the simplified result of the product expression. No brackets are required.

Constraints

All coefficients in any part of evaluation will be less than 10^9

The input contains no more than 10 simplified bracketed expressions

The input contains no more than 10 simplified bracketed expressions

Example

Input

(i+j)(k)

Output

i-j

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