Background

Xiao Ming has started middle school and always makes mistakes in polynomial calculations. Therefore, he has turned to you, a programming enthusiast, to design a program to help him.

Problem Description

Input several monomials or polynomials and compute the result.

Input Format

The input includes operators (+, -, *), letters (only lowercase letters from a to z), monomials without parentheses on both sides, and polynomials with parentheses ( ) or brackets [ ] on both sides. It is guaranteed that within each factor, monomials precede polynomials. (The length does not exceed 255 characters)

Output Format

Output the result of the expression, with each factor sorted lexicographically.

Sample Input and Output

Input Sample #1

(a+b)*(a+b+c)

Output Sample #1

a^2+2ab+ac+b^2+bc

Input Sample #2

(a+b)*(a+b+c)

Output Sample #2

a^2+2ab+ac+b^2+bc

Input Sample #3

(2a+b)*(2a-b)

Output Sample #3

4a^2-b^2

Input Sample #4

(a+b)*(a+b)*(a+b)

Output Sample #4

a^3+3a^2b+3ab^2+b^3

Input Sample #5

f*(a+b+d+z)+f^2

Output Sample #5

af+bf+df+fz+f^2

Input Sample #6

(a+b+2c)*(a+b-2c)-(a+b)*(a+b)

Output Sample #6

-4c^2

Notes

This is an easy problem.

见题面 Input 部分

见题面 Output 部分