Problem:
Score : 300 points

Problem Statement

Takahashi, Aoki and Snuke love cookies. They have A, B and C cookies, respectively. Now, they will exchange those cookies by repeating the action below:

Each person simultaneously divides his cookies in half and gives one half to each of the other two persons.

This action will be repeated until there is a person with odd number of cookies in hand.

How many times will they repeat this action?
Note that the answer may not be finite.

Constraints

1 ≤ A,B,C ≤ 10^9

Input

Input is given from Standard Input in the following format:

A B C

Output

Print the number of times the action will be performed by the three people, if this number is finite.
If it is infinite, print -1 instead.

Sample Input 1

4 12 20

Sample Output 1

3

Initially, Takahashi, Aoki and Snuke have 4, 12 and 20 cookies. Then,

After the first action, they have 16, 12 and 8.

After the second action, they have 10, 12 and 14.

After the third action, they have 13, 12 and 11.

Now, Takahashi and Snuke have odd number of cookies, and therefore the answer is 3.

Sample Input 2

14 14 14

Sample Output 2

-1

Sample Input 3

454 414 444

Sample Output 3

1

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)


#ifndef TEMPLATE_HPP
#define TEMPLATE_HPP

#include <algorithm>
#include <bitset>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <set>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define _GLIBCXX_DEBUG

// Utility
using std::declval;
using std::distance;
using std::enable_if_t;
using std::get;
using std::index_sequence;
using std::is_array;
using std::is_pointer;
using std::is_same;
using std::iterator_traits;
using std::make_index_sequence;
using std::make_pair;
using std::make_tuple;
using std::make_unique;
using std::random_access_iterator_tag;
using std::stold;
using std::stoll;
using std::operator""s;
using std::abs;

// Types
using std::bitset;
using std::deque;
using std::list;
using std::multiset;
using std::nullptr_t;
using std::pair;
using std::tuple;
using std::unordered_multimap;
using std::unordered_multiset;
using ll = /** __int128; //*/ long long int;
using lf = long double;
using str = std::string;
template <class T> using u_set = std::unordered_set<T>;
template <class T> using vec = std::vector<T>;
using vecl = vec<ll>;
using vecf = vec<lf>;
using vecs = vec<str>;
template <class K, class V> using u_map = std::unordered_map<K, V>;
template <class V> using graph = u_map<V, u_set<V>>;
template <typename _Signature> using fun = std::function<_Signature>;

// Algorithms
using std::accumulate;
using std::all_of;
using std::any_of;
using std::back_inserter;
using std::copy;
using std::copy_if;
using std::count;
using std::count_if;
using std::find_if;
using std::for_each;
using std::inserter;
using std::lower_bound;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::next_permutation;
using std::none_of;
using std::partial_sum;
using std::remove_if;
using std::replace_if;
using std::reverse;
using std::set_difference;
using std::set_intersection;
using std::set_symmetric_difference;
using std::set_union;
using std::sort;
using std::swap;
using std::transform;
using std::unique;
using std::upper_bound;

namespace utils {
str to_string(__int128 const &x) { return std::to_string((long long)x); }
template <class T> T clamp(T const &v, T const &l, T const &h) {
  return min(h, max(l, v));
}
ll gcd(ll p, ll q) { return (q == 0) ? p : gcd(q, p % q); }
ll lcm(ll p, ll q) { return p / gcd(q, p) * q; }
} // namespace utils
using std::to_string;
using utils::clamp;
using utils::gcd;
using utils::lcm;
using utils::to_string;

namespace io {
// Input
using IS = std::istream;
IS &in(IS &);
IS &in(IS &i) { return i; }
template <class T, class... Ts> IS &in(IS &i, T &a, Ts &... as) {
  return in(i >> a, as...);
}
IS &operator>>(IS &i, __int128 &x) {
  long long int xx;
  i >> xx;
  x = xx;
  return i;
}
template <class V> IS &operator>>(IS &i, vec<V> &a) {
  for (auto &ai : a)
    i >> ai;
  return i;
}
template <class F, class S> IS &operator>>(IS &i, pair<F, S> &p) {
  return i >> p.first >> p.second;
}
template <class... Ts> IS &operator>>(IS &i, tuple<Ts...> &t) {
  return apply([&](auto &... ts) -> IS & { return in(i, ts...); }, t);
}
// Output
using OS = std::ostream;
OS &out_join(OS &o, str const &) { return o; }
template <class T> OS &out_join(OS &o, str const &, T const &a) {
  return o << a;
}
template <class T, class... Ts>
OS &out_join(OS &o, str const &sep, T const &a, Ts const &... as) {
  return out_join(o << a << sep, sep, as...);
}
OS &operator<<(OS &o, __int128 const &x) { return o << (long long int)x; }
template <class F, class S> OS &operator<<(OS &o, pair<F, S> const &p) {
  return o << p.first << ":" << p.second;
}
template <class... Ts, size_t... I>
OS &tuple_out(OS &o, tuple<Ts...> const &t, index_sequence<I...>) {
  return out_join(o, ",", get<I>(t)...);
}
template <class... Ts> OS &operator<<(OS &o, tuple<Ts...> const &t) {
  return tuple_out(o << "(", t, make_index_sequence<sizeof...(Ts)>()) << ")";
}
template <class T> struct Joiner {
  str const pre;
  str const post;
  str const sep;
  vec<T> const container;
  template <class Itr>
  Joiner(Itr const &begin, Itr const &end, str const &sep, str const &pre,
         str const &post)
      : pre(pre), post(post), sep(sep), container(begin, end) {}
};
template <class T> OS &operator<<(OS &o, Joiner<T> const &joiner) {
  auto itr = joiner.container.begin();
  auto end = joiner.container.end();
  o << joiner.pre;
  if (itr != end)
    o << *(itr++);
  while (itr != end)
    o << joiner.sep << *(itr++);
  return o << joiner.post;
}
template <class Itr>
auto join(Itr const &b, Itr const &e, str const &sep = ""s,
          str const &pre = ""s, str const &post = ""s) {
  using T = typename iterator_traits<Itr>::value_type;
  return Joiner<T>(b, e, sep, pre, post);
}
template <class C, enable_if_t<!is_same<C, str>::value && !is_array<C>::value &&
                                   !is_pointer<C>::value &&
                                   !std::is_arithmetic<C>::value,
                               nullptr_t> = nullptr>
OS &operator<<(OS &o, C const &a) {
  return o << join(a.begin(), a.end(), ",", "[", "]");
}
} // namespace io
using std::cerr;
using std::cin;
using std::cout;
auto init_io = []() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cout << std::fixed << std::setprecision(15);
};
auto input = [](auto &... a) { io::in(cin, a...); };
auto print = [](auto const &... a) { io::out_join(cout, " ", a...) << "\n"; };
#ifdef JUMPAKU_DEBUG
auto dump = [](auto const &... a) { io::out_join(cerr, " "s, a...) << "\n"; };
#else
auto dump = [](auto const &...) {};
#endif
using io::join;

// Hash
namespace hashcode {
template <class... Ts> size_t hash_args(size_t h, Ts const &... ts);
size_t hash_args(size_t h) { return h; }
template <class T, class... Ts>
size_t hash_args(size_t h, T const &t, Ts const &... ts) {
  constexpr std::hash<T> hasher;
  return hash_args(((h << 19) - h) ^ hasher(t), ts...);
}
template <class... Ts, size_t... I>
size_t hash_tuple(tuple<Ts...> const &t, index_sequence<I...>) {
  return hash_args(17, get<I>(t)...);
}
} // namespace hashcode
namespace std {
#if __GNUC__ == 5 || defined(__STRICT_ANSI__)
template <> struct hash<__int128> {
  size_t operator()(__int128 const &t) const {
    return (t & 0xffffff) ^ ((t >> 63) & 0xffffff);
  }
};
#endif
template <class... Ts> struct hash<tuple<Ts...>> {
  size_t operator()(tuple<Ts...> const &t) const {
    size_t h = hashcode::hash_tuple(t, index_sequence_for<Ts...>());
    return h ^ (h >> 32);
  }
};
template <class T> struct hash<u_set<T>> {
  size_t operator()(u_set<T> const &t) const {
    constexpr std::hash<T> hasher;
    return accumulate(
        t.begin(), t.end(), (size_t)0,
        [&](auto acc, auto const &ti) { return acc + hasher(ti); });
  }
};
} // namespace std

// Range
namespace ranges {
template <class T, class Itr> struct iterator_base {
  using difference_type = ll;
  using value_type = T;
  using pointer = T *;
  using reference = T &;
  using iterator_category = random_access_iterator_tag;
  ll i;
  iterator_base(ll const &i) : i(i) {}
  bool operator==(Itr const &itr) const { return i == itr.i; }
  bool operator!=(Itr const &itr) const { return i != itr.i; }
  ll operator-(Itr const &itr) const { return i - itr.i; }
  Itr operator++(int) { return with(i++); }
  Itr operator--(int) { return with(i--); }
  Itr operator+(ll const &n) const { return with(i + n); }
  Itr operator-(ll const &n) const { return with(i - n); }
  Itr &operator+=(ll const &n) {
    i += n;
    return self();
  }
  Itr &operator-=(ll const &n) { return self() += (-n); }
  Itr &operator++() { return self() += 1; }
  Itr &operator--() { return self() -= 1; }

protected:
  virtual Itr with(ll i) const = 0;
  virtual Itr &self() = 0;
};
template <class T> struct seq_base {
  ll const b;
  ll const e;
  seq_base(ll b, ll e) : b(b), e(max(b, e)) {}
  ll size() const { return e - b; }
  bool empty() const { return size() == 0; }
};
template <class T> struct seq : seq_base<T> {
  struct iterator : iterator_base<T, iterator> {
    seq<T> const &s;
    iterator(seq<T> const &s, ll const &i)
        : iterator_base<T, iterator>(i), s(s) {}
    iterator(iterator const &) = default;
    iterator with(ll i) const override { return iterator(s, i); }
    iterator &self() override { return *this; }
    T operator*() const { return s[this->i]; }
    iterator &operator=(iterator const &itr) {
      this->i = itr.i;
      return *this;
    }
  };
  fun<T(ll)> const f;
  seq(ll b, ll e, fun<T(ll)> const &f) : seq_base<T>(b, e), f(f) {}
  iterator begin() const { return iterator(*this, 0); }
  iterator end() const { return iterator(*this, this->size()); }
  T operator[](ll i) const { return f(i + this->b); }
};

struct range : seq_base<ll> {
  struct iterator : iterator_base<ll, iterator> {
    iterator(ll const &i) : iterator_base<ll, iterator>(i) {}
    iterator with(ll i) const override { return iterator(i); }
    iterator &self() override { return *this; }
    ll operator*() const { return i; }
  };
  range(ll n) : range(0, n) {}
  range(ll b, ll e) : seq_base<ll>(b, e) {}
  iterator begin() const { return iterator(b); }
  iterator end() const { return iterator(e); }
  bool has(ll x) const { return b <= x && x < e; }
  ll operator[](ll i) const { return i + b; }
};
} // namespace ranges
using range = ranges::range;
range::iterator end(ll i) { return range::iterator(i); }
range::iterator begin(ll i = 0) { return range::iterator(i); }
template <class F> auto seq(ll n, F const &f) {
  using T = decltype(f(declval<ll>()));
  return ranges::seq<T>(0LL, n, f);
}

namespace optional {
template <class T> struct opt {
  std::unique_ptr<T> ptr;
  opt(nullptr_t ptr = nullptr) : ptr(ptr){};
  opt(T const &val) : ptr(make_unique<T>(val)){};
  opt(opt<T> const &o) : opt<T>(nullptr) {
    if (o)
      ptr = make_unique<T>(*o);
  }
  opt(opt<T> &&) = default;
  opt<T> &operator=(opt<T> const &o) {
    ptr = o ? make_unique<T>(*o) : nullptr;
    return *this;
  }
  opt<T> &operator=(opt<T> &&) = default;
  operator bool() const { return has_value(); }
  T &operator*() { return value(); }
  T const &operator*() const { return value(); }
  T *operator->() { return &(*ptr); }
  T const *operator->() const { return &(*ptr); }
  T &value() { return *ptr; }
  T const &value() const { return *ptr; }
  T value_or(T const &val) const { return (ptr) ? value() : val; }
  bool has_value() const { return ptr != nullptr; }
};
template <class T> io::OS &operator<<(io::OS &o, opt<T> const &opt) {
  using io::operator<<;
  return opt.has_value() ? (o << "Some(" << opt.value() << ")") : (o << "None");
}
} // namespace optional
using optional::opt;

bool odd(ll n) { return n & 1; }
bool even(ll n) { return !odd(n); }

bool imply(bool p, bool q) { return !p || q; }
bool iff(bool p, bool q) { return p == q; }

constexpr lf PI = 3.141592653589793238462643383279502884L;
constexpr ll MOD = 1e9 + 7;

#endif /* TEMPLATE_HPP */

/**
// DP Definition
using Data = struct {};
using Key = tuple<>;
using Value = ll;
using Cache = u_map<Key, Value>;
struct DP {
  Data data;
  Cache cache;
  DP(Data const &data) : data(data), cache((ll)1e6) {}
  Value compute(Key const &key) {
    if (IS_INITIAL)
      return INITIAL_VALUE;
    auto found = cache.find(key);
    if (found != cache.end())
      return found->second;
    return cache[key] = RECURSION_CALL(this->compute(Key{}));
  }
};
// DP Call
/*
  DP dp(Data{});
  print(dp.compute(Key{}));
*/

void solve();
int main(int, char *[]) {
  init_io();
  ll t = 1;
  /** input(t); /**/
  while (t--)
    solve();
  cout.flush();
}

void solve() {
  ll A, B, C;
  input(A, B, C);
  ll a = A, b = B, c = C;
  for (auto &&n : range(1e8)) {
    if (odd(a) || odd(b) || odd(c)) {
      print(n);
      return;
    }
    if (n > 0 && a == A && b == B && c == C) {
      print(-1);
      return;
    }
    ll a2 = a / 2, b2 = b / 2, c2 = c / 2;
    a = b2 + c2;
    b = a2 + c2;
    c = b2 + a2;
  }
}