George likes arithmetics very much. Especially he likes the integers series. His most favourite thing is the infinite sequence of digits, which results as the concatenation of all positive integers in ascending order. The beginning of this sequence is 1234567891011121314… Let us call this sequence S. Then S = 1, S = 2, …, S = 1, S = 0, …, and so on.
George takes a sequence of digits A and wants to know when it first appears in S. Help him to solve this difficult problem.
The first line contains A - the given sequence of digits. The number of digits in A does not exceed 200.
Output the only number - the least k such that A = S[k], A = S[k+1], ... A[len(A)] = S[k + len(A) – 1], where len(A) denotes the length of A (i.e. the number of digits in it).
Problem Author: Nikita Shamgunov
Problem Source: ACM ICPC 2001. Northeastern European Region, Northern Subregion