Is it truthy or falsy? There are so many different ways to express whether something is true or not! The goal of this challenge is to produce a standardized output of truthy or falsy for various input truthy and falsy values.

For the purposes of this challenge, the following inputs are considered truthy:


A string representing a signed integer with a non-zero value (contains only the digits [0-9], with an optional - at the beginning). Note that the string -0 will never be given as input. A non-zero integer will never be preceded by a 0 (i.e. 01 will never be given as input, similarly -01 will never be gien as input).
The case-insensitive strings equivalent to one of defined, found, nonnil, non-nil, on, success, t, true, y, and yes


For the purposes of this challenge, the following inputs are considered falsy:


The string 0. Repeated zeros (00, 00...) will never be given as input.
An empty string
The case-insensitive strings equivalent to one of f, failure, false, n, nan, nil, no, notfound, not-found, null, nullptr, off, and undefined


Input

The input is a string representing a truthy/falsy value. The string may come from any source desired (stdio, function parameter, etc.). There is no leading/trailing whitespace.

The input is guaranteed to match one of the allowed truthy/falsy values above (i.e. you do not need to provide any error handling).

Output

Your program/function must output a truthy/falsy value which represents the "truthy-ness" or "falsy-ness" of the input.
You are only allowed to specify exactly 1 truthy and 1 falsy value which your output must convert the input to (these are your "standardized" truthy/falsy value). The output may be written to any sink desired (stdio, return value, output parameter, etc.).

Please specify what truthy and falsy value you chose in your answer.

Ex.: If you choose the string true as a truthy value, you cannot also have the integer 1 for truthy.

Test Cases

Test cases are formatted as the first line is the input, and the second line is the output.

-1
true

1
true

1234
true

-4321
true

defined
true

deFined
true

Found
true

nonnil
true

non-nil
true

ON
true

SuCCess
true

T
true

true
true

y
true

YeS
true

0
false

'' (empty string)
false

faLSE
false

f
false

Failure
false

n
false

NaN
false

nil
false

no
false

notfound
false

not-Found
false

NULL
false

nullptr
false

OFF
false

unDefined
false


Scoring

This is code-golf; shortest code in bytes wins. Standard loopholes apply. You may use any built-ins desired.
MATL, 20 bytes
U|sG36ZA13\[BID1]m+g

Input is a string enclosed in single quotes. Output is 1 for truthy or 0 for falsy.
Try it online! Or verify all test cases.
How it works
U|s      % Take input implicitly. Interpret as number, absolute value, sum
G36ZA    % Push input again. Convert from base-36
13\      % Modulo 13
[BID1]   % Push array [6 3 8 1]
m        % True if member: gives 1 iff the result from modulo 13 is in the array
+g       % Add, convert to logical. Display implicitly

This performs two tests on the input:

Try to interpret the input as a number, and detect if it is nonzero. The function used to interpret a string as a number outputs an empty array if it's not possible; and the sum of the entries of an empty array is 0. So it suffices to try the conversion, take the absolute value, and sum. This gives a positive value if the input contains a nonzero number, and 0 otherwise.
Assuming the input string doesn't represent a number, we need to classify it into one of the two given sets. To do this, the input is interpreted as the digits of a number expressed in base-36, using alphabet '01...9ab...z'. The base conversion function is case-insensitive and ignores digits not present in the alphabet (in our case, '-'). It turns out that the modulo 13 of the resulting number is 1, 3, 6 or 8 for the truthy strings, and doesn't give any of those values for the falsy strings. So it can be used as a signature. We thus perform modulo 13 and see if the result is any of those four values. This gives 1 if it is, or 0 otherwise.

The final result should be truthy if any of the two conditions is met, and falsy otherwise. So we add the two numbers resulting from 1 and 2 above and convert to logical, which gives 1 or 0 as standardized truthy/falsy values.