Folded Numbers

You have to compute the value of “folding” a number. “Folding” a number $n$ is an operation shown in the following figure (open the PDF if you can’t see the figure correctly on the Jutge web page).

In particular, any number $n$ can be considered a sequence of digits and be divided into two subsequences of consecutive digits $a$ and $b$ , be they of the same length, or alternatively of lengths differing only in one unit (including the case where $a$ or $b$ are empty). Concatenating these two halves $a$ and $b$ we would recover the original number $n$ .

Then, to compute the "folding" operation, we invert the order of the $a$ subsequence, which we will call $a_{inv}$ , and, interpreting $a_{inv}$ and $b$ as numbers once again, add them together to obtain the result of "folding".

As an example, if $n$ is 1234, the subsequence $a$ is 12 and $b$ is 34. Inverting the order of $a$ gives 21, and the result will be, then, $21 + 34 = 55$ .

In the case where $n$ has an odd length, the partition can be made in two different ways. For instance, if $n$ is 12345, we can compute the "folding" in these two ways:

Divide $n$ in $a = 123$ and $b = 45$ , and inverting $a$ and adding, we would get $321 + 45 = 366$ .
Divide $n$ in $a = 12$ and $b = 345$ , and inverting $a$ and adding, we would get $21 + 345 = 366$ .

The middle digit, then, ends up contributing in the same way to the final sum in both cases.

Input

The input consists of a sequence of strictly positive integers.

Output

The output consists of each number in the input “folded” as explained, each one in a separate line.

Problem information

Author: PRO1

Generation: 2026-01-25T16:12:06.143Z