Actually, the \E is not needed, since $input is the only thing in the regex; that is, it is automatically ended.

/(\Q$input)/
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Here's a question: Why would you need to put parentheses around $input? You can access its value more efficiently as $input, than as $1, since parentheses would slow down the regex. More succintly, change the code to this:

/\Q$input/
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And change occurences of $1 to $input