P9080 [PA 2018] New Contract

**This problem is translated from [PA 2018](https://sio2.mimuw.edu.pl/c/pa-2018-1/dashboard/) Round 2 [Nowy kontrakt](https://sio2.mimuw.edu.pl/c/pa-2018-1/p/kon/)**. You are given a sequence $a$ of $N$ positive integers. You need to make the sequence **strictly increasing** by appending digits to the end of numbers in the sequence. Your goal is to minimize the number of appended digits. Appending a digit $t$ to a number $a$ means: $a \gets a \times 10 + t$, where $t \in \{0,1,2,3,4,5,6,7,8,9\}$.

The first line contains an integer $N$, the length of the sequence. Lines $2$ to $N + 1$ each contain one number. Line $i$ contains the $(i - 1)$-th number in the sequence.

Print one integer: the minimum number of operations.

#### Sample 1 Explanation Append one digit to the 2nd number and one digit to the 3rd number, i.e., $a_2 \gets a_2 \times 10 + 7$, $a_3 \gets a_3 \times 10 + 3$. The new sequence becomes $(8,57,133)$, which is strictly increasing. The number of operations is $2$. There are other ways with $2$ operations, but there is no way with only $1$ operation. ------------ #### Constraints **This problem uses bundled tests.** For $100\%$ of the testdata: - $1 \le N \le 200000$. - $1 \le a_i \le 10^9$. Translated by ChatGPT 5