F. Ones
dp; greedy; shortest paths
You are given a positive (greater than zero) integer \(n\).You have to represent \(n\) as the sum of integers (possibly negative) consisting only of ones (digits '1'). For example, \(24 = 11 + 11 + 1 + 1\) and \(102 = 111 - 11 + 1 + 1\). Among all possible representations, you have to find the one that uses the minimum number of ones in total.
The single line contains one integer \(n\) (\(1 \le n < 10^{50}\)).
Print one integer \(x\) — the minimum number of ones, such that there exist a representation of \(n\) as the sum of integers (possibly negative) that uses \(x\) ones in total.