A permutation of a set $S = {s_1, s_2, dotsc, s_n}$ is a bijective function $pi: S to S$. For example, if $S = {1,2,3,4}$ then the function $pi: x mapsto 1 + (x + 1 mod 4)$ is a permutation:

$$
pi(1) = 3,quad
pi(2) = 4,quad
pi(3) = 1,quad
pi(4) = 2
$$

We can also have permutations on infinite sets, let's take $mathbb{N}$ as an example: The function $pi: x mapsto x-1 + 2cdot(x mod 2)$ is a permutation, swapping the odd and even integers in blocks of two. The first elements are as follows:

$$
2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,dotsc
$$

Challenge

Your task for this challenge is to write a function/program implementing any¹ permutation on the positive natural numbers. The score of your solution is the sum of codepoints after mapping them with the implemented permutation.

Example

Suppose we take the above permutation implemented with Python:

def pi(x):

    return x - 1 + 2*(x % 2)

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The character d has codepoint $100$, $texttt{pi}(100) = 99$. If we do this for every character, we get:

$$
99,102,101,31,111,106,39,119,42,57,9,31,31,31,31,113,102,115,118,113,109,31,119,31,46,31,50,31,44,31,49,41,39,119,31,38,31,49,42
$$

The sum of all these mapped characters is $2463$, this would be the score for that function.

Rules

You will implement a permutation $pi$ either as a function or program

• given an natural number $x$, return/output $pi(x)$
  


• for the purpose of this challenge $mathbb{N}$ does not contain $0$
  


• the permutation must non-trivially permute an infinite subset of $mathbb{N}$
  


• your function/program is not allowed to read its own source

Scoring

The score is given by the sum of all codepoints (zero bytes may not be part of the source code) under that permutation (the codepoints depend on your language², you're free to use SBCS, UTF-8 etc. as long as your language supports it).

The submission with the lowest score wins, ties are broken by earliest submission.

_{1: Except for permutations which only permute a finite subset of $mathbb{N}$, meaning that the set ${ x | pi(x) neq x }$ must be infinite.}

_{2: If it improves your score, you can for example use a UTF-8 encoded Jelly submission instead of the usual SBCS.}

Jelly, score  288 250 212  199

-38 thanks to Erik the Outgolfer!

C-*+

Swaps even with odd.

The score is $67+45+44+43=199$ - see self-scoring here.

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JavaScript (ES6), Score =  276  268

$=>(--$^40)+!0

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Retina 0.8.2, 6 bytes, score 260

T`O`RO

Try it online! Link includes self-scoring footer. Simply swaps digits 1 and 9 and 3 and 7 in the decimal representations, so that numbers that contain no digits coprime to 10 are unaffected.

Perl 6, Score 804 615 576

{{($++∉ords(q[!$()+12?_doqrsx{}∉])??21+$++!!++$)xx$_+1}()[$_]}

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The first quine-y type answer here, and I think it scores pretty well. Anonymous code block that takes an integer and returns one.

This produces the sequence $21,22,23,24...$ with the sequence $1,2,3,4...20$ inserted at the indexes of the unique sorted codepoints of the code. For example, the 30th through 35th elements of the sequence are $51,52,53,1,54,55$ since the 33rd codepoint is !.

(This is 0-indexed, which might not be valid. I have a 1-indexed solution prepared)

A more trivial answer (but with a worse score):

Perl 6, Score: 647

{TR;52;25;}

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This swaps the digits 5 and 2 in the input, which mostly saves score on the ;52;25; part, which consists of code points in the 50-59 range (and increases the score of the {}, with codepoints 123 and 125)