Sequence of Comparisons

2000ms

262144K

Description:

Once upon a time, Petya had an array of integers $$$a$$$ of length $$$n$$$. But over time, the array itself was lost, and only $$$n-1$$$ results of comparisons of neighboring array elements remained. In other words, for every $$$i$$$ from $$$1$$$ to $$$n-1$$$, Petya knows exactly one of these three facts:

$$$a_i < a_{i+1}$$$;
$$$a_i = a_{i+1}$$$;
$$$a_i > a_{i+1}$$$.

Petya wonders if it is possible to uniquely determine the result of comparing $$$a_1$$$ and $$$a_n$$$.

You have to help Petya determine the result of comparing $$$a_1$$$ and $$$a_n$$$ or report that the result cannot be determined unambiguously.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases.

The only line of the test case contains the string $$$s$$$ ($$$1 \le |s| \le 100$$$), where $$$s_i$$$ is:

<, if $$$a_i < a_{i + 1}$$$;
>, if $$$a_i > a_{i + 1}$$$;
=, if $$$a_i = a_{i + 1}$$$.

Output:

For each test case, print a single string equal to:

<, if $$$a_1 < a_n$$$;
>, if $$$a_1 > a_n$$$;
=, if $$$a_1 = a_n$$$;
?, if it is impossible to uniquely determine the result of the comparison.

Sample Input:

4
>>>
<><=<
=
<<==

Sample Output:

>
?
=
<

Note:

Consider the test cases of the example:

in the first test case, it's easy to see that $$$a_1 > a_4$$$ since $$$a_1 > a_2 > a_3 > a_4$$$;
in the second test case, both sequences $$$[1, 2, 0, 10, 10, 15]$$$ and $$$[10, 11, 1, 2, 2, 5]$$$ meet the constraints; in the first one, $$$a_1 < a_6$$$, and in the second one, $$$a_1 > a_6$$$, so it's impossible to compare $$$a_1$$$ and $$$a_6$$$;
in the third test case, we already know that $$$a_1 = a_2$$$;
in the fourth test case, it's easy to see that $$$a_3 = a_4 = a_5$$$, and $$$a_1 < a_2 < a_3$$$, so $$$a_1 < a_5$$$.

Informação

Provedor Codeforces

Código CF1571A