Problem J
Exponentiation
There are $n$ integer variables $x_1, x_2, \dots , x_n$. At the start, each variable is set to $2023$. You have to perform $m$ instructions of the following two types:
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Operations, of the form “! $i$ $j$”, where $i \neq j$. This means that $x_i$ gets set to $x_i^{x_j}$.
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Queries, of the form “? $i$ $j$”, where $i \neq j$. This means that you should print ‘>’ if $x_i$ is greater than $x_j$, ‘=’ if $x_i$ is equal to $x_j$, and ‘<’ if $x_i$ is smaller than $x_j$.
Consider the first sample. After the $5$ operations, the values of the variables are:
\begin{align*} x_1& =\left({2023}^{2023}\right)^{{2023}^{2023}},& x_2& =\left({2023}^{{2023}^{2023}}\right)^{2023},& x_3& ={2023},& x_4& ={2023}^{2023}. \end{align*}Input
The input consists of:
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One line with two integers $n$ and $m$ ($2 \leq n \leq 1000$, $1 \leq m \leq 1000$), the number of variables and the number of instructions.
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$m$ lines, each containing a character $c$ (either ‘!’ or ‘?’) and two integers $i$ and $j$ ($1 \leq i, j \leq n$, $i \neq j$), describing the instructions.
Output
For every query in the input, output its answer.
| Sample Input 1 | Sample Output 1 |
|---|---|
4 8 ! 1 4 ! 2 1 ! 4 3 ! 1 4 ! 2 3 ? 3 4 ? 2 4 ? 2 1 |
< > = |
| Sample Input 2 | Sample Output 2 |
|---|---|
4 9 ! 2 4 ! 1 2 ? 3 1 ? 1 2 ! 2 3 ? 1 2 ! 1 3 ! 3 2 ? 1 3 |
< > > < |
