1515: CF83 - E. Two Subsequences
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Description
On an IT lesson Valera studied data compression. The teacher told about a new method, which we shall now describe to you.
Let {$a_1,a_2,...,a_n$} be the given sequence of lines needed to be compressed. Here and below we shall assume that all lines are of the same length and consist only of the digits $0$ and $1$. Let's define the compression function:
Note that it is not allowed to change the relative order of lines in the subsequences. It is allowed to make one of the subsequences empty. Each string from the initial sequence should belong to exactly one subsequence. Elements of subsequences $b$ and $c$ don't have to be consecutive in the original sequence $a$, i. e. elements of $b$ and $c$ can alternate in $a$ (see samples 2 and 3).
Help Valera to find the minimum possible value of $S$.
- $f$(empty sequence)=empty string
- $f(s)=s$.
- $f(s_1,s_2)=$ the smallest in length string, which has one of the prefixes equal to $s_1$ and one of the suffixes equal to $s_2$. For example, $f$(001,011)=0011, $f$(111,011)=111011.
- $f(a_1,a_2,...,a_n)=f(f(a_1,a_2,a_{n-1}),a_n)$. For example, $f$(000,000,111)=$f(f$(000,000),111)=$f$(000,111)=000111.
Note that it is not allowed to change the relative order of lines in the subsequences. It is allowed to make one of the subsequences empty. Each string from the initial sequence should belong to exactly one subsequence. Elements of subsequences $b$ and $c$ don't have to be consecutive in the original sequence $a$, i. e. elements of $b$ and $c$ can alternate in $a$ (see samples 2 and 3).
Help Valera to find the minimum possible value of $S$.
Input
The first line of input data contains an integer $n$ − the number of strings $(1≤n≤2·10^5)$.
Then on $n$ lines follow elements of the sequence − strings whose lengths are from $1$ to $20$ characters, consisting only of digits $0$ and $1$. The $i+1$-th input line contains the $i$-th element of the sequence. Elements of the sequence are separated only by a newline. It is guaranteed that all lines have the same length.
Then on $n$ lines follow elements of the sequence − strings whose lengths are from $1$ to $20$ characters, consisting only of digits $0$ and $1$. The $i+1$-th input line contains the $i$-th element of the sequence. Elements of the sequence are separated only by a newline. It is guaranteed that all lines have the same length.
Output
Print a single number − the minimum possible value of $S$.
Sample 1 Input
3
01
10
01
Sample 1 Output
4
The best option is to make one of the subsequences empty, and the second one equal to the whole given sequence. $|f(01,10,01)|=|f(f(01,10),01)|=|f(010,01)|=|0101|=4$.
Sample 2 Input
4
000
111
110
001
Sample 2 Output
8
The best option is: b={000,001},c={111,110}.S=|f(000,001)|+|f(111,110)|=|0001|+|1110|=8.
Sample 3 Input
5
10101
01010
11111
01000
10010
Sample 3 Output
17
The best option is:b={10101,01010,01000},c={11111,10010}.S=|10101000|+|111110010|=17.