Make a String

You have an initially empty string $S$, a target string $T$ and a sequence of $n$ strings $p_1, p_2, \dots, p_n$. You may perform any number of operations; let's denote by $|S|$ the length of the string $S$ before the current operation. Each operation should be of one of the following types: - insert a lowercase English letter $x$ at the beginning of the string $S$; the cost of this operation is