From 99042fd37af04144da0984dc7f436b3b89cb934c Mon Sep 17 00:00:00 2001
From: Matej Focko <mfocko@redhat.com>
Date: Wed, 28 Feb 2024 12:26:23 +0100
Subject: [PATCH] 1933: add solutions from the contest

Signed-off-by: Matej Focko <mfocko@redhat.com>
---
 1933/a.cpp | 340 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1933/b.cpp | 355 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1933/c.cpp | 347 +++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 1042 insertions(+)
 create mode 100644 1933/a.cpp
 create mode 100644 1933/b.cpp
 create mode 100644 1933/c.cpp

diff --git a/1933/a.cpp b/1933/a.cpp
new file mode 100644
index 0000000..b07062f
--- /dev/null
+++ b/1933/a.cpp
@@ -0,0 +1,340 @@
+#pragma region includes
+#include <algorithm>
+#include <array>
+#include <bit>
+#include <bitset>
+#include <cassert>
+#include <cctype>
+#include <chrono>
+#include <cmath>
+#include <cstdint>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <map>
+#include <numeric>
+#include <optional>
+#include <queue>
+#include <random>
+#include <set>
+#include <sstream>
+#include <string>
+#include <vector>
+#pragma endregion includes
+
+#pragma region helpers
+
+#pragma region aliases
+#define LOOP(var, n) for (auto var = 0; var < n; ++var)
+
+template <typename T>
+using V = std::vector<T>;
+
+template <typename K, typename V>
+using M = std::map<K, V>;
+
+template <typename T>
+using S = std::set<T>;
+
+template <typename T>
+using Q = std::deque<T>;
+
+using i8 = std::int8_t;
+using u8 = std::uint8_t;
+using i16 = std::int16_t;
+using u16 = std::uint16_t;
+using i32 = std::int32_t;
+using u32 = std::uint32_t;
+using i64 = std::int64_t;
+using u64 = std::uint64_t;
+#pragma endregion /* aliases */
+
+#pragma region data structures
+template <typename T>
+struct max_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end());
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end());
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+
+template <typename T>
+struct min_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end(), std::greater<>{});
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end(), std::greater<>{});
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+#pragma endregion /* data structures */
+
+#pragma region debug
+void dbg_out() { std::cerr << std::endl; }
+template <typename Head, typename... Tail>
+void dbg_out(Head H, Tail... T) {
+  std::cerr << ' ' << H;
+  dbg_out(T...);
+}
+#ifdef LOCAL
+#define dbg(...)                                                           \
+  std::cerr << '[' << __FILE__ << ':' << __LINE__ << "] (" << #__VA_ARGS__ \
+            << "):",                                                       \
+      dbg_out(__VA_ARGS__)
+#else
+#define dbg(...)
+#endif
+#pragma endregion debug
+
+#pragma region functional
+// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
+template <class Fun>
+class y_combinator_result {
+  Fun fun_;
+
+ public:
+  template <class T>
+  explicit y_combinator_result(T &&fun) : fun_(std::forward<T>(fun)) {}
+  template <class... Args>
+  decltype(auto) operator()(Args &&...args) {
+    return fun_(std::ref(*this), std::forward<Args>(args)...);
+  }
+};
+template <class Fun>
+decltype(auto) y_combinator(Fun &&fun) {
+  return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
+}
+#pragma endregion /* functional */
+
+#pragma region input
+template <typename Container>
+void collect(Container &c, std::size_t size) {
+  auto it = std::inserter(c, c.begin());
+
+  for (auto i = 0u; i < size; ++i) {
+    typename Container::value_type x;
+    std::cin >> x;
+    it = std::move(x);
+  }
+}
+
+template <typename Container>
+Container collect(std::size_t size) {
+  Container c{};
+  collect(c, size);
+  return c;
+}
+
+template <typename T>
+std::map<T, std::size_t> collect_count(std::size_t size) {
+  std::map<T, std::size_t> counts;
+
+  for (auto i = 0u; i < size; ++i) {
+    T x;
+    std::cin >> x;
+    ++counts[x];
+  }
+
+  return counts;
+}
+#pragma endregion /* input */
+
+#pragma region math
+long pow(long base, long exp) {
+  if (exp == 0) return 1;
+  long half = pow(base, exp / 2);
+  if (exp % 2 == 0) return half * half;
+  return half * half * base;
+}
+
+template <typename T>
+T isqrt(T x) {
+  assert(x >= 0);
+
+  auto max_shift = 8 * sizeof(T) - 1;
+  auto shift = (max_shift - std::countl_zero(x)) & ~1;
+  auto bit = 1 << shift;
+
+  T result = 0;
+  while (bit != 0) {
+    if (x >= (result + bit)) {
+      x -= result + bit;
+      result = (result >> 1) + bit;
+    } else {
+      result = (result >> 1);
+    }
+    bit = bit >> 2;
+  }
+
+  return result;
+}
+
+template <std::int64_t MODULO = 1000000007>
+struct Z {
+  Z(std::int64_t x = 0) : x(x % MODULO) {}
+
+  Z pow(std::uint32_t exp) const {
+    auto ans = 1;
+    auto base = x;
+
+    for (; exp > 0; exp >>= 1) {
+      if (exp % 2 == 1) {
+        ans *= base;
+      }
+
+      base *= base;
+    }
+
+    return ans;
+  }
+
+  Z inv() const {
+    assert(x != 0);
+    return pow(MODULO - 2);
+  }
+
+  Z operator-() const { return {-x}; }
+  Z operator+=(const Z &rhs) { x = (x + rhs.x) % MODULO; }
+  Z operator-=(const Z &rhs) { x = (x - rhs.x) % MODULO; }
+  Z operator*=(const Z &rhs) { x = (x * rhs.x) % MODULO; }
+  Z operator/=(const Z &rhs) { x = (x * rhs.inv().x) % MODULO; }
+
+  friend Z operator+(Z lhs, const Z &rhs) { return lhs += rhs; }
+  friend Z operator-(Z lhs, const Z &rhs) { return lhs -= rhs; }
+  friend Z operator*(Z lhs, const Z &rhs) { return lhs *= rhs; }
+  friend Z operator/(Z lhs, const Z &rhs) { return lhs /= rhs; }
+
+  friend std::istream &operator>>(std::istream &is, Z &z) {
+    is >> z.x;
+    z.x %= MODULO;
+    return is;
+  }
+
+  friend std::ostream &operator<<(std::ostream &os, const Z &z) {
+    return os << z.x;
+  }
+
+ private:
+  std::int64_t x;
+};
+#pragma endregion /* math */
+
+#pragma region output
+template <typename T, typename U>
+std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
+  return os << p.first << " " << p.second;
+}
+
+template <typename C, typename T = typename std::enable_if<
+                          !std::is_same<C, std::string>::value,
+                          typename C::value_type>::type>
+std::ostream &operator<<(std::ostream &os, const C &v) {
+  std::string sep;
+  for (const T &x : v) {
+    os << sep << x, sep = " ";
+  }
+
+  return os;
+}
+
+template <typename T>
+inline void answer(const T &ans) {
+#ifdef LOCAL
+  std::cout << "Answer: ";
+#endif
+
+  std::cout << ans << "\n";
+}
+
+inline void yes() { answer("YES"); }
+inline void no() { answer("NO"); }
+inline void yesno(bool ans) { answer(ans ? "YES" : "NO"); }
+#pragma endregion /* output */
+
+#pragma region rng
+std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
+#pragma endregion /* rng */
+
+#pragma endregion /* helpers */
+
+// for ‹N› test cases, uncomment for single test case
+// #define SINGLE
+
+namespace solution {
+
+using namespace std;
+
+void solve() {
+  size_t n;
+  cin >> n;
+
+  V<int> a;
+  collect(a, n);
+
+  long long int sum = 0;
+  for (const auto x: a) {
+    sum += abs(x);
+  }
+  answer(sum);
+}
+
+void tests() {
+  // TODO
+}
+
+}  // namespace solution
+
+using namespace solution;
+
+#ifdef TEST
+
+int main(void) {
+  tests();
+  return 0;
+}
+
+#else
+
+int main(void) {
+  int N = 1;
+
+#ifndef SINGLE
+
+  std::cin >> N;
+
+#endif
+
+  while (N-- > 0) {
+    solve();
+  }
+
+  return 0;
+}
+
+#endif
diff --git a/1933/b.cpp b/1933/b.cpp
new file mode 100644
index 0000000..e65c744
--- /dev/null
+++ b/1933/b.cpp
@@ -0,0 +1,355 @@
+#pragma region includes
+#include <algorithm>
+#include <array>
+#include <bit>
+#include <bitset>
+#include <cassert>
+#include <cctype>
+#include <chrono>
+#include <cmath>
+#include <cstdint>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <map>
+#include <numeric>
+#include <optional>
+#include <queue>
+#include <random>
+#include <set>
+#include <sstream>
+#include <string>
+#include <vector>
+#pragma endregion includes
+
+#pragma region helpers
+
+#pragma region aliases
+#define LOOP(var, n) for (auto var = 0; var < n; ++var)
+
+template <typename T>
+using V = std::vector<T>;
+
+template <typename K, typename V>
+using M = std::map<K, V>;
+
+template <typename T>
+using S = std::set<T>;
+
+template <typename T>
+using Q = std::deque<T>;
+
+using i8 = std::int8_t;
+using u8 = std::uint8_t;
+using i16 = std::int16_t;
+using u16 = std::uint16_t;
+using i32 = std::int32_t;
+using u32 = std::uint32_t;
+using i64 = std::int64_t;
+using u64 = std::uint64_t;
+#pragma endregion /* aliases */
+
+#pragma region data structures
+template <typename T>
+struct max_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end());
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end());
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+
+template <typename T>
+struct min_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end(), std::greater<>{});
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end(), std::greater<>{});
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+#pragma endregion /* data structures */
+
+#pragma region debug
+void dbg_out() { std::cerr << std::endl; }
+template <typename Head, typename... Tail>
+void dbg_out(Head H, Tail... T) {
+  std::cerr << ' ' << H;
+  dbg_out(T...);
+}
+#ifdef LOCAL
+#define dbg(...)                                                           \
+  std::cerr << '[' << __FILE__ << ':' << __LINE__ << "] (" << #__VA_ARGS__ \
+            << "):",                                                       \
+      dbg_out(__VA_ARGS__)
+#else
+#define dbg(...)
+#endif
+#pragma endregion debug
+
+#pragma region functional
+// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
+template <class Fun>
+class y_combinator_result {
+  Fun fun_;
+
+ public:
+  template <class T>
+  explicit y_combinator_result(T &&fun) : fun_(std::forward<T>(fun)) {}
+  template <class... Args>
+  decltype(auto) operator()(Args &&...args) {
+    return fun_(std::ref(*this), std::forward<Args>(args)...);
+  }
+};
+template <class Fun>
+decltype(auto) y_combinator(Fun &&fun) {
+  return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
+}
+#pragma endregion /* functional */
+
+#pragma region input
+template <typename Container>
+void collect(Container &c, std::size_t size) {
+  auto it = std::inserter(c, c.begin());
+
+  for (auto i = 0u; i < size; ++i) {
+    typename Container::value_type x;
+    std::cin >> x;
+    it = std::move(x);
+  }
+}
+
+template <typename Container>
+Container collect(std::size_t size) {
+  Container c{};
+  collect(c, size);
+  return c;
+}
+
+template <typename T>
+std::map<T, std::size_t> collect_count(std::size_t size) {
+  std::map<T, std::size_t> counts;
+
+  for (auto i = 0u; i < size; ++i) {
+    T x;
+    std::cin >> x;
+    ++counts[x];
+  }
+
+  return counts;
+}
+#pragma endregion /* input */
+
+#pragma region math
+long pow(long base, long exp) {
+  if (exp == 0) return 1;
+  long half = pow(base, exp / 2);
+  if (exp % 2 == 0) return half * half;
+  return half * half * base;
+}
+
+template <typename T>
+T isqrt(T x) {
+  assert(x >= 0);
+
+  auto max_shift = 8 * sizeof(T) - 1;
+  auto shift = (max_shift - std::countl_zero(x)) & ~1;
+  auto bit = 1 << shift;
+
+  T result = 0;
+  while (bit != 0) {
+    if (x >= (result + bit)) {
+      x -= result + bit;
+      result = (result >> 1) + bit;
+    } else {
+      result = (result >> 1);
+    }
+    bit = bit >> 2;
+  }
+
+  return result;
+}
+
+template <std::int64_t MODULO = 1000000007>
+struct Z {
+  Z(std::int64_t x = 0) : x(x % MODULO) {}
+
+  Z pow(std::uint32_t exp) const {
+    auto ans = 1;
+    auto base = x;
+
+    for (; exp > 0; exp >>= 1) {
+      if (exp % 2 == 1) {
+        ans *= base;
+      }
+
+      base *= base;
+    }
+
+    return ans;
+  }
+
+  Z inv() const {
+    assert(x != 0);
+    return pow(MODULO - 2);
+  }
+
+  Z operator-() const { return {-x}; }
+  Z operator+=(const Z &rhs) { x = (x + rhs.x) % MODULO; }
+  Z operator-=(const Z &rhs) { x = (x - rhs.x) % MODULO; }
+  Z operator*=(const Z &rhs) { x = (x * rhs.x) % MODULO; }
+  Z operator/=(const Z &rhs) { x = (x * rhs.inv().x) % MODULO; }
+
+  friend Z operator+(Z lhs, const Z &rhs) { return lhs += rhs; }
+  friend Z operator-(Z lhs, const Z &rhs) { return lhs -= rhs; }
+  friend Z operator*(Z lhs, const Z &rhs) { return lhs *= rhs; }
+  friend Z operator/(Z lhs, const Z &rhs) { return lhs /= rhs; }
+
+  friend std::istream &operator>>(std::istream &is, Z &z) {
+    is >> z.x;
+    z.x %= MODULO;
+    return is;
+  }
+
+  friend std::ostream &operator<<(std::ostream &os, const Z &z) {
+    return os << z.x;
+  }
+
+ private:
+  std::int64_t x;
+};
+#pragma endregion /* math */
+
+#pragma region output
+template <typename T, typename U>
+std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
+  return os << p.first << " " << p.second;
+}
+
+template <typename C, typename T = typename std::enable_if<
+                          !std::is_same<C, std::string>::value,
+                          typename C::value_type>::type>
+std::ostream &operator<<(std::ostream &os, const C &v) {
+  std::string sep;
+  for (const T &x : v) {
+    os << sep << x, sep = " ";
+  }
+
+  return os;
+}
+
+template <typename T>
+inline void answer(const T &ans) {
+#ifdef LOCAL
+  std::cout << "Answer: ";
+#endif
+
+  std::cout << ans << "\n";
+}
+
+inline void yes() { answer("YES"); }
+inline void no() { answer("NO"); }
+inline void yesno(bool ans) { answer(ans ? "YES" : "NO"); }
+#pragma endregion /* output */
+
+#pragma region rng
+std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
+#pragma endregion /* rng */
+
+#pragma endregion /* helpers */
+
+// for ‹N› test cases, uncomment for single test case
+// #define SINGLE
+
+namespace solution {
+
+using namespace std;
+
+void solve() {
+  size_t n;
+  cin >> n;
+
+  V<int> a;
+  collect(a, n);
+
+  V<int> counters(3, 0);
+
+  long long int sum = 0;
+  for (const auto x: a) {
+    ++counters[x % 3];
+    sum += x;
+  }
+
+  auto rem = sum % 3;
+  if (rem == 0) {
+    answer(0);
+    return;
+  }
+
+  if (counters[rem] > 0) {
+    answer(1);
+    return;
+  }
+
+  answer(3 - rem);
+}
+
+void tests() {
+  // TODO
+}
+
+}  // namespace solution
+
+using namespace solution;
+
+#ifdef TEST
+
+int main(void) {
+  tests();
+  return 0;
+}
+
+#else
+
+int main(void) {
+  int N = 1;
+
+#ifndef SINGLE
+
+  std::cin >> N;
+
+#endif
+
+  while (N-- > 0) {
+    solve();
+  }
+
+  return 0;
+}
+
+#endif
diff --git a/1933/c.cpp b/1933/c.cpp
new file mode 100644
index 0000000..5a288ac
--- /dev/null
+++ b/1933/c.cpp
@@ -0,0 +1,347 @@
+#pragma region includes
+#include <algorithm>
+#include <array>
+#include <bit>
+#include <bitset>
+#include <cassert>
+#include <cctype>
+#include <chrono>
+#include <cmath>
+#include <cstdint>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <map>
+#include <numeric>
+#include <optional>
+#include <queue>
+#include <random>
+#include <set>
+#include <sstream>
+#include <string>
+#include <vector>
+#pragma endregion includes
+
+#pragma region helpers
+
+#pragma region aliases
+#define LOOP(var, n) for (auto var = 0; var < n; ++var)
+
+template <typename T>
+using V = std::vector<T>;
+
+template <typename K, typename V>
+using M = std::map<K, V>;
+
+template <typename T>
+using S = std::set<T>;
+
+template <typename T>
+using Q = std::deque<T>;
+
+using i8 = std::int8_t;
+using u8 = std::uint8_t;
+using i16 = std::int16_t;
+using u16 = std::uint16_t;
+using i32 = std::int32_t;
+using u32 = std::uint32_t;
+using i64 = std::int64_t;
+using u64 = std::uint64_t;
+#pragma endregion /* aliases */
+
+#pragma region data structures
+template <typename T>
+struct max_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end());
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end());
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+
+template <typename T>
+struct min_heap {
+  using container = std::vector<T>;
+
+  typename container::size_type size() const { return h.size(); }
+
+  void push(T item) {
+    h.push_back(item);
+    std::push_heap(h.begin(), h.end(), std::greater<>{});
+  }
+
+  T pop() {
+    std::pop_heap(h.begin(), h.end(), std::greater<>{});
+    T item = std::move(h.back());
+    h.pop_back();
+    return item;
+  }
+
+ private:
+  container h;
+};
+#pragma endregion /* data structures */
+
+#pragma region debug
+void dbg_out() { std::cerr << std::endl; }
+template <typename Head, typename... Tail>
+void dbg_out(Head H, Tail... T) {
+  std::cerr << ' ' << H;
+  dbg_out(T...);
+}
+#ifdef LOCAL
+#define dbg(...)                                                           \
+  std::cerr << '[' << __FILE__ << ':' << __LINE__ << "] (" << #__VA_ARGS__ \
+            << "):",                                                       \
+      dbg_out(__VA_ARGS__)
+#else
+#define dbg(...)
+#endif
+#pragma endregion debug
+
+#pragma region functional
+// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
+template <class Fun>
+class y_combinator_result {
+  Fun fun_;
+
+ public:
+  template <class T>
+  explicit y_combinator_result(T &&fun) : fun_(std::forward<T>(fun)) {}
+  template <class... Args>
+  decltype(auto) operator()(Args &&...args) {
+    return fun_(std::ref(*this), std::forward<Args>(args)...);
+  }
+};
+template <class Fun>
+decltype(auto) y_combinator(Fun &&fun) {
+  return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
+}
+#pragma endregion /* functional */
+
+#pragma region input
+template <typename Container>
+void collect(Container &c, std::size_t size) {
+  auto it = std::inserter(c, c.begin());
+
+  for (auto i = 0u; i < size; ++i) {
+    typename Container::value_type x;
+    std::cin >> x;
+    it = std::move(x);
+  }
+}
+
+template <typename Container>
+Container collect(std::size_t size) {
+  Container c{};
+  collect(c, size);
+  return c;
+}
+
+template <typename T>
+std::map<T, std::size_t> collect_count(std::size_t size) {
+  std::map<T, std::size_t> counts;
+
+  for (auto i = 0u; i < size; ++i) {
+    T x;
+    std::cin >> x;
+    ++counts[x];
+  }
+
+  return counts;
+}
+#pragma endregion /* input */
+
+#pragma region math
+long pow(long base, long exp) {
+  if (exp == 0) return 1;
+  long half = pow(base, exp / 2);
+  if (exp % 2 == 0) return half * half;
+  return half * half * base;
+}
+
+template <typename T>
+T isqrt(T x) {
+  assert(x >= 0);
+
+  auto max_shift = 8 * sizeof(T) - 1;
+  auto shift = (max_shift - std::countl_zero(x)) & ~1;
+  auto bit = 1 << shift;
+
+  T result = 0;
+  while (bit != 0) {
+    if (x >= (result + bit)) {
+      x -= result + bit;
+      result = (result >> 1) + bit;
+    } else {
+      result = (result >> 1);
+    }
+    bit = bit >> 2;
+  }
+
+  return result;
+}
+
+template <std::int64_t MODULO = 1000000007>
+struct Z {
+  Z(std::int64_t x = 0) : x(x % MODULO) {}
+
+  Z pow(std::uint32_t exp) const {
+    auto ans = 1;
+    auto base = x;
+
+    for (; exp > 0; exp >>= 1) {
+      if (exp % 2 == 1) {
+        ans *= base;
+      }
+
+      base *= base;
+    }
+
+    return ans;
+  }
+
+  Z inv() const {
+    assert(x != 0);
+    return pow(MODULO - 2);
+  }
+
+  Z operator-() const { return {-x}; }
+  Z operator+=(const Z &rhs) { x = (x + rhs.x) % MODULO; }
+  Z operator-=(const Z &rhs) { x = (x - rhs.x) % MODULO; }
+  Z operator*=(const Z &rhs) { x = (x * rhs.x) % MODULO; }
+  Z operator/=(const Z &rhs) { x = (x * rhs.inv().x) % MODULO; }
+
+  friend Z operator+(Z lhs, const Z &rhs) { return lhs += rhs; }
+  friend Z operator-(Z lhs, const Z &rhs) { return lhs -= rhs; }
+  friend Z operator*(Z lhs, const Z &rhs) { return lhs *= rhs; }
+  friend Z operator/(Z lhs, const Z &rhs) { return lhs /= rhs; }
+
+  friend std::istream &operator>>(std::istream &is, Z &z) {
+    is >> z.x;
+    z.x %= MODULO;
+    return is;
+  }
+
+  friend std::ostream &operator<<(std::ostream &os, const Z &z) {
+    return os << z.x;
+  }
+
+ private:
+  std::int64_t x;
+};
+#pragma endregion /* math */
+
+#pragma region output
+template <typename T, typename U>
+std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
+  return os << p.first << " " << p.second;
+}
+
+template <typename C, typename T = typename std::enable_if<
+                          !std::is_same<C, std::string>::value,
+                          typename C::value_type>::type>
+std::ostream &operator<<(std::ostream &os, const C &v) {
+  std::string sep;
+  for (const T &x : v) {
+    os << sep << x, sep = " ";
+  }
+
+  return os;
+}
+
+template <typename T>
+inline void answer(const T &ans) {
+#ifdef LOCAL
+  std::cout << "Answer: ";
+#endif
+
+  std::cout << ans << "\n";
+}
+
+inline void yes() { answer("YES"); }
+inline void no() { answer("NO"); }
+inline void yesno(bool ans) { answer(ans ? "YES" : "NO"); }
+#pragma endregion /* output */
+
+#pragma region rng
+std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
+#pragma endregion /* rng */
+
+#pragma endregion /* helpers */
+
+// for ‹N› test cases, uncomment for single test case
+// #define SINGLE
+
+namespace solution {
+
+using namespace std;
+
+auto count_ks(S<int>& ks, int l, int a, int b) -> int {
+  ks.insert(l);
+
+  if (l % a == 0) {
+    count_ks(ks, l / a, a, b);
+  }
+  if (l % b == 0) {
+    count_ks(ks, l / b, a, b);
+  }
+
+  return static_cast<int>(ks.size());
+}
+
+void solve() {
+  int a, b, l;
+  cin >> a >> b >> l;
+
+  S<int> ks;
+  answer(count_ks(ks, l, a, b));
+}
+
+void tests() {
+  // TODO
+}
+
+}  // namespace solution
+
+using namespace solution;
+
+#ifdef TEST
+
+int main(void) {
+  tests();
+  return 0;
+}
+
+#else
+
+int main(void) {
+  int N = 1;
+
+#ifndef SINGLE
+
+  std::cin >> N;
+
+#endif
+
+  while (N-- > 0) {
+    solve();
+  }
+
+  return 0;
+}
+
+#endif