A cyclic number with $n$ digits has a very interesting property:
When it is multiplied by $1,2,3,4,\dots ,n$, all the products have exactly the same digits, in the same order, but rotated in a circular fashion!

The smallest cyclic number is the $6$-digit number $142857$:
$142857\times 1=142857$
$142857\times 2=285714$
$142857\times 3=428571$
$142857\times 4=571428$
$142857\times 5=714285$
$142857\times 6=857142$

The next cyclic number is $0588235294117647$ with $16$ digits :
$0588235294117647\times 1=0588235294117647$
$0588235294117647\times 2=1176470588235294$
$0588235294117647\times 3=1764705882352941$
$\dots$
$0588235294117647\times 16=9411764705882352$

Note that for cyclic numbers, leading zeros are important.

There is only one cyclic number for which, the eleven leftmost digits are $00000000137$ and the five rightmost digits are $56789$ (i.e., it has the form $00000000137\cdots 56789$ with an unknown number of digits in the middle). Find the sum of all its digits.