Simple Prefix Compression

Many databases store character fields (and especially indices) using prefix compression. This technique compresses a sequence of strings $A_1, A_2, \ldots, A_N$ as follows.

The first string $A_1$ is stored in full. For every subsequent string $A_{i+1}$, let $j$ be the length of the longest common prefix it shares with the previous string $A_i$ — the largest $j \le \min(p, q)$ such that the first $j$ characters of $A_i = a_{i,1} a_{i,2} \cdots a_{i,p}$ and $A_{i+1} = a_{i+1,1} a_{i+1,2} \cdots a_{i+1,q}$ are equal. Then $A_{i+1}$ is stored as a single control character whose code is $j$, followed by the remaining characters $a_{i+1,j+1} a_{i+1,j+2} \cdots a_{i+1,q}$. Its stored length is therefore $1 + (q - j)$.

If $j = 0$ (the two strings have no common prefix), the string is still prefixed by one control byte, so its stored length is one greater than its original length.

Compute the minimal total stored length of the whole sequence.

The first line contains an integer $N$. Each of the next $N$ lines contains one string $A_i$.

Print a single integer: the minimal total length of the compressed strings.

• $1 \le N \le 10000$
• $1 \le \operatorname{length}(A_i) \le 255$