1565: CF825 - F. String Compression
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Description
Ivan wants to write a letter to his friend. The letter is a string $s$ consisting of lowercase Latin letters.
Unfortunately, when Ivan started writing the letter, he realised that it is very long and writing the whole letter may take extremely long time. So he wants to write the compressed version of string $s$ instead of the string itself.
The compressed version of string $s$ is a sequence of strings $c_1,s_1,c_2,s_2,...,c_k,s_k$, where $c_i$ is the decimal representation of number $a_i$ (without any leading zeroes) and $s_i$ is some string consisting of lowercase Latin letters. If Ivan writes string $s_1$ exactly $a_1$ times, then string $s_2$ exactly $a_2$ times, and so on, the result will be strings.
The length of a compressed version is $|c_1|+|s_1|+|c_2|+|s_2|... |c_k|+|s_k|$. Among allcompressed versionsIvan wants to choose a version such that its length is minimum possible. Help Ivan to determine minimum possible length.
The compressed version of string $s$ is a sequence of strings $c_1,s_1,c_2,s_2,...,c_k,s_k$, where $c_i$ is the decimal representation of number $a_i$ (without any leading zeroes) and $s_i$ is some string consisting of lowercase Latin letters. If Ivan writes string $s_1$ exactly $a_1$ times, then string $s_2$ exactly $a_2$ times, and so on, the result will be strings.
The length of a compressed version is $|c_1|+|s_1|+|c_2|+|s_2|... |c_k|+|s_k|$. Among allcompressed versionsIvan wants to choose a version such that its length is minimum possible. Help Ivan to determine minimum possible length.
Input
The only line of input contains one string $s$ consisting of lowercase Latin letters $(1≤|s|≤8000)$.
Output
Output one integer number − the minimum possible length of a compressed version of $s$.
Sample 1 Input
aaaaaaaaaa
Sample 1 Output
3
Ivan will choose this compressed version: $c_1$ is 10, $s_1$ is a.
Sample 2 Input
abcab
Sample 2 Output
6
Ivan will choose this compressed version:$c_1$ is 1, $s_1$ is abcab.
Sample 3 Input
cczabababab
Sample 3 Output
7
Ivan will choose this compressed version: $c_1$ is 2, $s_1$ is c, $c_2$ is 1, $s_2$ is z, $c_3$ is 4, $s_3$ is ab.