Average Substring Value

문제

Let $ss$ be a nonempty string consisting entirely of base-$1010$ digits (0-9). If the length of $ss$ is $n,n,$ number the digits $1,2,3,\dots ,n1,\; 2,\; 3,\; \backslash ldots,\; n$ from left to right, and for $1\le i\le j\le n,1\; \backslash leq\; i\; \backslash leq\; j\; \backslash leq\; n,$ let $s[i,j]s[i,j]$ denote the substring consisting of the digits from position $ii$ to position $jj$, inclusive. (It follows that we are only considering nonempty substrings.) Assign a value to each substring that is simply equal to the largest digit in the substring. What is the average value of the substrings of $ss$?

Note that two different substrings may be identical (as strings), but for the purposes of this problem they are treated as distinct. For example, if $s=s\; =$1010, then $s[1,2]=s[3,4]=s[1,2]\; =\; s[3,4]\; =$10 are distinct substrings (both with value $11$).

입력

The input is a single nonempty string, $s,s,$ of base-$1010$ digits. The length of $ss$ is at most $200000200\backslash ,000$.

출력

Output a line containing the average value of the substrings of $ss$. If the average is an integer, print the integer. If the average is a proper fraction, i.e., is equal to $a\mathrm{/}ba/b$, where $aa$ and $bb$ are positive integers and , print this fraction in lowest terms, with a '/' symbol separating the numerator and denominator. If the average is greater than $11$ and does not simplify to an integer, print the whole part followed by the proper fractional part, separated by a space, with the proper fractional part in lowest terms and formatted as described in the previous sentence.