Problem:
Score: 500 points

Problem Statement

In the Kingdom of AtCoder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1, 10, 10^2, 10^3, \dots, 10^{(10^{100})}. You have come shopping at a mall and are now buying a takoyaki machine with a value of N. (Takoyaki is the name of a Japanese snack.)

To make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N.

What will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count?

Assume that you have sufficient numbers of banknotes, and so does the clerk.

Constraints

N is an integer between 1 and 10^{1,000,000} (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum possible number of total banknotes used by you and the clerk.

Sample Input 1

36

Sample Output 1

8

If you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used.

The payment cannot be made with less than eight banknotes in total, so the answer is 8.

Sample Input 2

91

Sample Output 2

3

If you give two banknotes of value 100, 1, and the clerk gives you back one banknote of value 10, a total of three banknotes are used.

Sample Input 3

314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170

Sample Output 3

243

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdint.h>
#include <stdlib.h>

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
using namespace std;
using default_counter_t = int64_t;

// macro
#define let auto const&
#define overload4(a, b, c, d, name, ...) name
#define rep1(n) \
  for (default_counter_t i = 0, end_i = default_counter_t(n); i < end_i; ++i)
#define rep2(i, n)                                                           \
  for (default_counter_t i = 0, end_##i = default_counter_t(n); i < end_##i; \
       ++i)
#define rep3(i, a, b)                                    \
  for (default_counter_t i       = default_counter_t(a), \
                         end_##i = default_counter_t(b); \
       i < end_##i; ++i)
#define rep4(i, a, b, c)                                 \
  for (default_counter_t i       = default_counter_t(a), \
                         end_##i = default_counter_t(b); \
       i < end_##i; i += default_counter_t(c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep1(n) \
  for (default_counter_t i = default_counter_t(n) - 1; i >= 0; --i)
#define rrep2(i, n) \
  for (default_counter_t i = default_counter_t(n) - 1; i >= 0; --i)
#define rrep3(i, a, b)                                         \
  for (default_counter_t i         = default_counter_t(b) - 1, \
                         begin_##i = default_counter_t(a);     \
       i >= begin_##i; --i)
#define rrep4(i, a, b, c)                                          \
  for (default_counter_t                                           \
           i = (default_counter_t(b) - default_counter_t(a) - 1) / \
                   default_counter_t(c) * default_counter_t(c) +   \
               default_counter_t(a),                               \
           begin_##i = default_counter_t(a);                       \
       i >= begin_##i; i -= default_counter_t(c))
#define rrep(...) \
  overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)

#define ALL(f, c, ...)                                           \
  (([&](decltype((c)) cccc) {                                    \
    return (f)(std::begin(cccc), std::end(cccc), ##__VA_ARGS__); \
  })(c))

// function
template <class C>
constexpr C& Sort(C& a) {
  std::sort(std::begin(a), std::end(a));
  return a;
}
template <class C>
constexpr auto& Min(C const& a) {
  return *std::min_element(std::begin(a), std::end(a));
}
template <class C>
constexpr auto& Max(C const& a) {
  return *std::max_element(std::begin(a), std::end(a));
}
template <class C>
constexpr auto Total(C const& c) {
  return std::accumulate(std::begin(c), std::end(c), C(0));
}
template <typename T>
auto CumSum(std::vector<T> const& v) {
  std::vector<T> a(v.size() + 1, T(0));
  for (std::size_t i = 0; i < a.size() - size_t(1); ++i) a[i + 1] = a[i] + v[i];
  return a;
}
template <typename T>
constexpr bool ChMax(T& a, T const& b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
constexpr bool ChMin(T& a, T const& b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

void In(void) { return; }

template <typename First, typename... Rest>
void In(First& first, Rest&... rest) {
  cin >> first;
  In(rest...);
  return;
}

template <class T, typename I>
void VectorIn(vector<T>& v, const I n) {
  v.resize(size_t(n));
  rep(i, v.size()) cin >> v[i];
}

void Out(void) {
  cout << "\n";
  return;
}

template <typename First, typename... Rest>
void Out(First first, Rest... rest) {
  cout << first << " ";
  Out(rest...);
  return;
}

constexpr auto yes(const bool c) { return c ? "yes" : "no"; }
constexpr auto Yes(const bool c) { return c ? "Yes" : "No"; }
constexpr auto YES(const bool c) { return c ? "YES" : "NO"; }

#ifdef USE_STACK_TRACE_LOGGER
#ifdef __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Weverything"
#include <glog/logging.h>
#pragma clang diagnostic pop
#endif  //__clang__
#endif  // USE_STACK_TRACE_LOGGER

int64_t f(int64_t x) { return (x == 9 ? 1 : x + 1); }
int64_t g(int64_t x) {
  int64_t a = x + 1;
  int64_t b = 10 - x;

  return min(a, b);
}
int64_t h(int64_t x) {
  int64_t a = x + 2;
  int64_t b = 10 - x - 1;

  return min(a, b);
}
signed main(int argc, char* argv[]) {
  (void)argc;
#ifdef USE_STACK_TRACE_LOGGER
  google::InitGoogleLogging(argv[0]);
  google::InstallFailureSignalHandler();
#else
  (void)argv;
#endif  // USE_STACK_TRACE_LOGGER
  string N_;
  In(N_);
  int64_t p = int64_t(N_.size());
  vector<int64_t> N(p);
  rep(i, p) N[i] = N_[i] - '0';

  vector<vector<int64_t>> dp(
      p, vector<int64_t>(2, numeric_limits<int64_t>::max()));

  dp[0][0] = N[0];
  dp[0][1] = f(N[0]);

  rep(i, 1, p) {
    ChMin(dp[i][0], dp[i - 1][0] + N[i]);
    ChMin(dp[i][1], dp[i - 1][0] + f(N[i]));
    ChMin(dp[i][0], dp[i - 1][1] + g(N[i]));
    ChMin(dp[i][1], dp[i - 1][1] + h(N[i]));
  }

  cout << min(dp[p - 1][0], dp[p - 1][1] + 1) << endl;

  return EXIT_SUCCESS;
}