That would be because your protected string r_input is not set.
First thing you need to understand is the Page Lifecycle - refer:
MSDN - ASP.Net Page Life Cycle Overview[
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Use your debugger & put a break point in btnSubmit_Click event.
Check what the value of r_input is (an empty string) & then look at the value of your input, somewhat confusingly named "input" - it will have whatever value the user has entered.
Kind Regards