#P1571A. Sequence of Comparisons
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ID: 6063
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Sequence of Comparisons
No submission language available for this problem.
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.
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 $a_i = a_{i + 1}$.
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.
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.
Samples
4
>>>
<><=<
=
<<==
>
?
=
<
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 $a_1 < a_5$.