utils/scrapers/prescraped/codeforces/Problems/1986D

You are given a string $$$s$$$ of length $$$n > 1$$$, consisting of digits from $$$0$$$ to $$$9$$$. You must insert exactly $$$n - 2$$$ symbols $$$+$$$ (addition) or $$$\times$$$ (multiplication) into this string to form a valid arithmetic expression.In this problem, the symbols cannot be placed before the first or after the last character of the string $$$s$$$, and two symbols cannot be written consecutively. Also, note that the order of the digits in the string cannot be changed. Let's consider $$$s = 987009$$$: From this string, the following arithmetic expressions can be obtained: $$$9 \times 8 + 70 \times 0 + 9 = 81$$$, $$$98 \times 7 \times 0 + 0 \times 9 = 0$$$, $$$9 + 8 + 7 + 0 + 09 = 9 + 8 + 7 + 0 + 9 = 33$$$. Note that the number $$$09$$$ is considered valid and is simply transformed into $$$9$$$. From this string, the following arithmetic expressions cannot be obtained: $$$+9 \times 8 \times 70 + 09$$$ (symbols should only be placed between digits), $$$98 \times 70 + 0 + 9$$$ (since there are $$$6$$$ digits, there must be exactly $$$4$$$ symbols).The result of the arithmetic expression is calculated according to the rules of mathematics — first all multiplication operations are performed, then addition. You need to find the minimum result that can be obtained by inserting exactly $$$n - 2$$$ addition or multiplication symbols into the given string $$$s$$$.