Formatting a Polynomial

Given a univariate polynomial expressed as

$$f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,\quad a_n\ne0, $$

each term is represented by its exponent and coefficient. Your task is to output the polynomial as a string following these rules:

1. The variable is x and the terms must be arranged in descending order of exponent.
2. Omit any term whose coefficient is 0.
3. If the highest degree term has a positive coefficient, do not print a leading '+'; if it is negative, start with a '-' sign.
4. For non-leading terms, prefix with '+' (if the coefficient is positive) or '-' (if negative). Follow the sign immediately with the absolute value of the coefficient (as a positive integer) except when the term's absolute coefficient is 1 and the exponent is greater than 0 (in which case omit the number).

5. The format for the variable part:

   • If the exponent \(b > 1\), output it as x^b (i.e. x^b in latex: \(x^b\)).
   • If the exponent is exactly 1, output it as x.
   • If the exponent is 0, output only the coefficient.
6. No extra spaces should appear at the beginning or end of the output string.

Note: The input always contains at least one non-zero coefficient and the highest degree term has a non-zero coefficient.

inputFormat

The first line contains an integer n representing the number of terms. The following n lines each contain two integers: the exponent and the coefficient of a term, separated by a space.

outputFormat

Output the formatted polynomial string as described.

sample

3
2 1
1 2
0 3

x^2+2x+3