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First, I have to say a sad thing... This number is very salad.


notation

This notation is lower compatible of arrow and chain notation.

First, I use 4 signs: \leftarrow,\rightarrow,\uparrow,\downarrow.

And see this table:

Lv1

Lv2

arrowy

\uparrow

\downarrow

chainy

\rightarrow

\leftarrow


Definitions of words

command is a sequence of arrows.

\uparrow and \downarrow are arrowy.

\leftarrow and \rightarrow are chainy.


Definitions of notations

In and below this section, capital letters are command and small letters are numbers.

Commands are defined from right to left.


If the last one is arrowy

If the command is made with one arrow,

a\uparrow b=a^b

a\downarrow b=a\uparrow^{b}a

Otherwise,

aC\uparrow b=aCaC...(btimes a's)...Ca

aC\downarrow b=aCaC...(btimes a's)...Ca

If the last one is chainy

If the last one is same as the one before last:

aC\rightarrow b C\rightarrow c=aC\rightarrow (aC\rightarrow (b-1) C\rightarrow c) C\rightarrow c-1

(note: this rule is same if the last arrows are \leftarrow .)

(note2: If any 1's is in this notation, after that,, including the one,, is deleted.)

Otherwise:

aC\rightarrow b=aC\uparrow b

aC\leftarrow b=a\rightarrow^{b}a


This is hard to understand, so I will give you an example.

3\leftarrow\leftarrow3

=3\leftarrow\uparrow3

=3\leftarrow3\leftarrow3

=3\leftarrow(3\leftarrow2\leftarrow3)\leftarrow2

=3\leftarrow(3\leftarrow(3\leftarrow1\leftarrow3)\leftarrow2)\leftarrow2

=3\leftarrow(3\leftarrow3\leftarrow2)\leftarrow2

=...



Just writing notaions is not fun. Last but not least, I will write a number:

Unreasonable number = 3\rightarrow\downarrow\uparrow\rightarrow\rightarrow\downarrow\rightarrow\rightarrow\uparrow\uparrow\downarrow\downarrow\leftarrow\rightarrow\leftarrow\rightarrow3

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