Compare Continued Fractions

In this problem, you compare two rational numbers given by their continued fractions.

A finite continued fraction is a sequence $[a_{0}; a_{1}, a_{2}, \ldots, a_{n}]$ with these restrictions:

• $n$ is a non-negative finite integer.
• The elements $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ are integers.
• $a_{i} > 0$ for each $i > 0$.
• $a_{n} > 1$ if $n > 0$.

These restrictions give a one-to-one correspondence between rational numbers and finite continued fractions. Each rational number $x$ corresponds to the unique continued fraction $[a_{0}; a_{1}, a_{2}, \ldots, a_{n}]$ such that

$x = a_{0} + \frac{1}{a_{1} + \frac{1}{a_{2} + \frac{1}{\ddots + \frac{1}{a_{n}}}}}$

We write this as $x = [a_{0}; a_{1}, a_{2}, \ldots, a_{n}]$. For example,

$\frac{17}{25} = 0 + \frac{1}{\frac{25}{17}} = 0 + \frac{1}{1 + \frac{8}{17}} = 0 + \frac{1}{1 + \frac{1}{\frac{17}{8}}} = \mathbf{0} + \frac{1}{\mathbf{1} + \frac{1}{\mathbf{2} + \frac{1}{\mathbf{8}}}}$

so $\frac{17}{25} = [0; 1, 2, 8]$.

Given the continued fractions for two rational numbers $x$ and $y$, determine whether $x < y$, $x = y$, or $x > y$.

The input has two lines. The first line contains the continued fraction for $x$. The second line contains the continued fraction for $y$.

Each continued fraction is a sequence of integers separated by single spaces. The first integer is $n$, the length of the continued fraction ($0 \le n \le 100\,000$). It is followed by $n + 1$ integers $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ ($|a_{i}| \le 10^{9}$). It is guaranteed that $a_{i} > 0$ for each $i > 0$, and $a_{n} > 1$ if $n > 0$.

On the first line, print one character: "<" if $x < y$, "=" if $x = y$, or ">" if $x > y$.