## Goal

The quaternions belong to a number system that extends the complex numbers. A quaternion is defined by the sum of scalar multiples of the constants i,j,k and 1.

More information is available at http://mathworld.wolfram.com/Quaternion.html

Consider the following properties:

jk = i

ki = j

ij = k

i² = j² = k² = -1

These properties also imply that:

kj = -i

ik = -j

ji = -k

The order of multiplication is important.

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

**Pay attention to the formatting**

The coefficient is appended to the left of the constant.

If a coefficient is 1 or -1, don't include the 1 symbol.

If a coefficient or scalar term is 0, don't include it.

The terms must be displayed in order: ai + bj + ck + d.

**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