結果
| 問題 | No.2929 Miracle Branch |
| ユーザー |
 りすりす/TwoSquirrels
|
| 提出日時 | 2024-10-12 16:59:26 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 54 ms / 2,000 ms |
| コード長 | 23,046 bytes |
| コンパイル時間 | 13,553 ms |
| コンパイル使用メモリ | 521,108 KB |
| 実行使用メモリ | 17,288 KB |
| 最終ジャッジ日時 | 2024-10-12 17:00:51 |
| 合計ジャッジ時間 | 21,013 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 23 ms
16,540 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 2 ms
5,248 KB |
| testcase_10 | AC | 2 ms
5,248 KB |
| testcase_11 | AC | 2 ms
5,248 KB |
| testcase_12 | AC | 2 ms
5,248 KB |
| testcase_13 | AC | 2 ms
5,248 KB |
| testcase_14 | AC | 2 ms
5,248 KB |
| testcase_15 | AC | 2 ms
5,248 KB |
| testcase_16 | AC | 2 ms
5,248 KB |
| testcase_17 | AC | 3 ms
5,248 KB |
| testcase_18 | AC | 2 ms
5,248 KB |
| testcase_19 | AC | 3 ms
5,248 KB |
| testcase_20 | AC | 3 ms
5,248 KB |
| testcase_21 | AC | 5 ms
5,248 KB |
| testcase_22 | AC | 2 ms
5,248 KB |
| testcase_23 | AC | 6 ms
5,248 KB |
| testcase_24 | AC | 16 ms
7,396 KB |
| testcase_25 | AC | 4 ms
5,248 KB |
| testcase_26 | AC | 2 ms
5,248 KB |
| testcase_27 | AC | 3 ms
5,248 KB |
| testcase_28 | AC | 22 ms
16,780 KB |
| testcase_29 | AC | 24 ms
16,652 KB |
| testcase_30 | AC | 23 ms
16,752 KB |
| testcase_31 | AC | 24 ms
16,776 KB |
| testcase_32 | AC | 23 ms
16,652 KB |
| testcase_33 | AC | 24 ms
16,644 KB |
| testcase_34 | AC | 52 ms
17,200 KB |
| testcase_35 | AC | 50 ms
17,284 KB |
| testcase_36 | AC | 23 ms
16,648 KB |
| testcase_37 | AC | 51 ms
17,288 KB |
| testcase_38 | AC | 49 ms
17,160 KB |
| testcase_39 | AC | 52 ms
17,288 KB |
| testcase_40 | AC | 51 ms
17,280 KB |
| testcase_41 | AC | 51 ms
17,284 KB |
| testcase_42 | AC | 54 ms
17,156 KB |
| testcase_43 | AC | 50 ms
17,124 KB |
| testcase_44 | AC | 49 ms
17,132 KB |
| testcase_45 | AC | 22 ms
16,616 KB |
ソースコード
// SPDX-License-Identifier: MIT
// (c) 2023 TwoSquirrels
// my AtCoder environment: https://github.com/TwoSquirrels/atcoder-env
//#define DEBUG
// enable debug mode when compiled with -DDEBUG
#ifdef DEBUG
# define IS_DEBUG (1)
#else
// QCFium method
# pragma GCC target("avx2")
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
# pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
# define IS_DEBUG (0)
#endif
/// includes
// standard libraries
#if __has_include(<bits/stdc++.h>)
# include <bits/stdc++.h>
#else // <bits/stdc++.h>
// C++17 (clang)
# include <cassert>
# include <cfenv>
# include <cfloat>
# include <ciso646>
# include <clocale>
# include <csetjmp>
# include <csignal>
# include <cstdbool>
# include <cinttypes>
# include <charconv>
# include <typeindex>
# include <any>
# include <scoped_allocator>
# include <forward_list>
# include <list>
# include <map>
# include <set>
# include <valarray>
# include <variant>
# include <unordered_map>
# include <unordered_set>
# include <queue>
# include <condition_variable>
# include <shared_mutex>
# include <codecvt>
# include <future>
# include <regex>
# include <iostream>
# include <random>
# include <ctgmath>
# include <fstream>
#endif // <bits/stdc++.h>
/// abi
#if __has_include(<cxxabi.h>)
# define INCLUDED_CXXABI
# include <cxxabi.h>
#endif // <cxxabi.h>
// boost libraries
#if __has_include(<boost/multiprecision/cpp_int.hpp>)
# define INCLUDED_BOOST_CPP_INT
# include <boost/multiprecision/cpp_int.hpp>
#endif
#if __has_include(<boost/math/special_functions/prime.hpp>)
# define INCLUDED_BOOST_PRIME
# include <boost/math/special_functions/prime.hpp>
#endif
#if __has_include(<boost/multiprecision/miller_rabin.hpp>)
# define INCLUDED_BOOST_MILLER_RABIN
# include <boost/multiprecision/miller_rabin.hpp>
#endif
// atcoder libraries
#if __has_include(<atcoder/all>)
# define INCLUDED_ACL
# include <atcoder/all>
#endif
/// sfinae
// is_pair
template <typename T> inline constexpr bool is_pair_v = false;
template <typename T, typename U> inline constexpr bool is_pair_v<std::pair<T, U>> = true;
// is_tuple
template <typename T> inline constexpr bool is_tuple_v = false;
template <typename... Types> inline constexpr bool is_tuple_v<std::tuple<Types...>> = true;
// istreamable
#if __cplusplus >= 202002L
template <typename T> concept istreamable_v = requires (T a) { std::cin >> a; };
#else // C++20
template<typename T, typename = void> inline constexpr bool istreamable_v = false;
template<typename T>
inline constexpr bool istreamable_v<T, std::void_t<decltype(std::cin >> std::declval<T&>())>> = true;
#endif // C++20
// ostreamable
#if __cplusplus >= 202002L
template <typename T> concept ostreamable_v = requires (T a) { std::cout << a; };
#else // C++20
template<typename T, typename = void> inline constexpr bool ostreamable_v = false;
template<typename T>
inline constexpr bool ostreamable_v<T, std::void_t<decltype(std::cout << std::declval<T&>())>> = true;
#endif // C++20
// iterable
#if __cplusplus >= 202002L
# if __has_include(<ranges>)
template <typename T> concept iterable_v = std::ranges::range<T>;
# else // <ranges>
template <typename T> concept iterable_v = requires (T a) { std::begin(a); std::end(a); };
# endif // C++20
#else // C++20
template <typename T> inline constexpr bool iterable_v =
std::is_same_v<decltype(std::begin(std::declval<T>())), decltype(std::end(std::declval<T>()))>;
#endif // C++20
/// utils
template <typename T> inline std::string get_typename(std::size_t length_limit = std::string::npos) {
std::string name;
#ifdef INCLUDED_CXXABI
name = abi::__cxa_demangle(typeid(T).name(), nullptr, nullptr, nullptr);
#else // INCLUDED_CXXABI
name = typeid(T).name();
#endif // INCLUDED_CXXABI
#ifdef __ANDROID__
name = std::regex_replace(name, std::regex("::__ndk1::"), "::");
#endif // __ANDROID__
if (name.length() > length_limit) name = name.substr(0, length_limit - 3) + "...";
return name;
}
template <typename T> constexpr T inf() {
if constexpr (std::numeric_limits<T>::has_infinity) return std::numeric_limits<T>::infinity();
return std::numeric_limits<T>::max() / 2.125L;
}
template <typename T> constexpr int sin90(T theta90) {
if (theta90 % 2 == 0) return 0;
return (theta90 % 4 + 4) % 4 < 2 ? 1 : -1;
}
template <typename T> constexpr int cos90(T theta90) {
return sin90(theta90 + 1);
}
template <typename T> constexpr int sin45(T theta45) {
if (theta45 % 4 == 0) return 0;
return (theta45 % 8 + 8) % 8 < 4 ? 1 : -1;
}
template <typename T> constexpr int cos45(T theta45) {
return sin45(theta45 + 2);
}
template <typename T, typename U> inline bool chmin(T &&a, const U b) {
const bool compare = a > b;
if (compare) a = b;
return compare;
}
template <typename T, typename U> inline bool chmax(T &&a, const U b) {
const bool compare = a < b;
if (compare) a = b;
return compare;
}
long long powi(int base, int exponent = 2) {
long long ans = 1;
for (int i = exponent; i != 0; i += (i >= 0 ? -1 : 1)) {
if (i >= 0) ans *= base;
else ans /= base;
if (ans == 0) break;
}
return ans;
}
#ifdef INCLUDED_ACL
template <typename T = atcoder::modint>
T mint_inv(T x) {
constexpr int memo_limit = 1 << 24;
static std::array<T, memo_limit> memo;
if (x.val() >= memo_limit) return x.inv();
if (memo[x.val()] == 0) memo[x.val()] = x.inv();
return memo[x.val()];
}
#endif // INCLUDED_ACL
template <typename T> bool is_prime(T n) {
if (n <= 1) return false;
if (n == 2 || n == 3) return true;
if (n % 2 == 0 || n % 3 == 0) return false;
// miller rabin
#ifdef INCLUDED_ACL
if (n <= std::min(1LL << 32, static_cast<long long>(std::numeric_limits<int>::max()))) {
return atcoder::internal::is_prime_constexpr(n);
}
#endif // INCLUDED_ACL
#ifdef INCLUDED_BOOST_MILLER_RABIN
return boost::multiprecision::miller_rabin_test(n, 25);
#endif // INCLUDED_BOOST_MILLER_RABIN
// binary search
#ifdef INCLUDED_BOOST_PRIME
if (n <= boost::math::prime(boost::math::max_prime)) {
int left = 0, right = boost::math::max_prime + 1;
while (right - left > 1) {
auto mid = (left + right) / 2;
(boost::math::prime(mid) <= n ? left : right) = mid;
}
return n == boost::math::prime(left);
}
#endif // INCLUDED_BOOST_PRIME
// trial
T tried = 3;
#ifdef INCLUDED_BOOST_PRIME
for (int i = 2; i <= int(boost::math::max_prime); i++) {
const auto prime_i = boost::math::prime(i);
if (prime_i > n / prime_i) return true;
if (n % prime_i == 0) return false;
tried = prime_i;
}
#endif // INCLUDED_BOOST_PRIME
for (T i = (tried + 5) / 6 * 6; (i - 1) * (i - 1) <= n; i += 6) {
if (n % (i - 1) == 0 || n % (i + 1) == 0) return false;
}
return true;
}
// thanks to https://perogram.hateblo.jp/entry/2019/03/29/193632
template <bool osa_k = false, typename T> std::vector<std::pair<T, int>> factors(T n) {
constexpr int spf_limit = 1 << 24;
std::vector<std::pair<T, int>> result;
if (n < 0) {
result.emplace_back(-1, 1);
const auto natural = factors<osa_k>(-n);
result.insert(result.end(), natural.begin(), natural.end());
} else if (n == 0) result.emplace_back(0, 1);
else if (n == 1);
else if (osa_k && n < spf_limit) {
static std::array<int, spf_limit> spf;
if (spf[0] == 0) {
for (int i = 0; i < spf_limit; i++) spf[i] = i % 2 == 0 ? 2 : i % 3 == 0 ? 3 : i;
spf[0] = 1;
for (int p1 = 6; (p1 - 1) * (p1 - 1) <= spf_limit; p1 += 6) {
if (spf[p1 - 1] == p1 - 1) for (int i = p1 - 1; i < spf_limit; i += p1 - 1) if (spf[i] == i) spf[i] = p1 - 1;
if (spf[p1 + 1] == p1 + 1) for (int i = p1 + 1; i < spf_limit; i += p1 + 1) if (spf[i] == i) spf[i] = p1 + 1;
}
}
while (n != 1) {
if (!result.empty() && result.back().first == spf[n]) result.back().second++;
else result.emplace_back(spf[n], 1);
n /= spf[n];
}
} else {
int expo = 0;
while (n % 2 == 0) { n /= 2; expo++; }
if (expo != 0) result.emplace_back(2, expo);
expo = 0;
while (n % 3 == 0) { n /= 3; expo++; }
if (expo != 0) result.emplace_back(3, expo);
T tried = 3;
#ifdef INCLUDED_BOOST_PRIME
for (int i = 2; i <= int(boost::math::max_prime); i++) {
const auto prime_i = boost::math::prime(i);
if (prime_i > n / prime_i) break;
expo = 0;
while (n % prime_i == 0) { n /= prime_i; expo++; }
result.emplace_back(prime_i, expo);
tried = prime_i;
}
if (osa_k && n < spf_limit) {
const auto rest = factors<osa_k>(n);
result.insert(result.end(), rest.begin(), rest.end());
n = 1;
}
#endif // INCLUDED_BOOST_PRIME
if (is_prime(n)) { result.emplace_back(n, 1); n = 1; }
for (T i = (tried + 5) / 6 * 6; (i - 1) * (i - 1) <= n; i += 6) {
expo = 0;
while (n % (i - 1) == 0) { n /= (i - 1); expo++; }
if (expo != 0) result.emplace_back(i - 1, expo);
expo = 0;
while (n % (i + 1) == 0) { n /= (i + 1); expo++; }
if (expo != 0) result.emplace_back(i + 1, expo);
if (osa_k && n < spf_limit) {
const auto rest = factors<osa_k>(n);
result.insert(result.end(), rest.begin(), rest.end());
n = 1;
}
}
if (n != 1) result.emplace_back(n, 1);
}
return result;
}
template <bool osa_k = false, typename T> std::vector<T> divisors(T n) {
std::vector<T> result(1, 1);
for (auto [prime, expo] : factors<osa_k>(n)) {
const int result_size = result.size();
T pow_i = 1;
for (int i = 1; i <= expo; i++) {
pow_i *= prime;
for (int k = 0; k < result_size; k++) result.emplace_back(result[k] * pow_i);
}
}
std::sort(result.begin(), result.end());
return result;
}
template <typename T> T fact(int n, bool inv = false) {
assert(n >= 0);
static std::vector<std::pair<T, T>> factorials = { { 1, 1 } };
for (int i = factorials.size(); i <= n; i++) factorials.emplace_back(i * factorials[i - 1].first, 0);
if (inv && factorials[n].second == 0) {
if constexpr (std::is_integral_v<T>) factorials[n].second = factorials[n].first <= 1 ? 1 : 0;
#ifdef INCLUDED_ACL
else if constexpr (atcoder::internal::is_modint<T>::value) factorials[n].second = mint_inv(factorials[n].first);
#endif // INCLUDED_ACL
else factorials[n].second = 1 / factorials[n].first;
}
return inv ? factorials[n].second : factorials[n].first;
}
template <typename T> T perm(int n, int k) { return fact<T>(n) * fact<T>(n - k, true); }
template <typename T> T comb(int n, int k) { return perm<T>(n, k) * fact<T>(k, true); }
// TODO: compressor
/*template <typename T> struct compressor {
std::vector<T> positions;
compressor() = default;
compressor(const std::vector<T> &initial_pos) {
}
};*/
template <typename T> std::vector<std::vector<T>> rotate(std::vector<std::vector<T>> grid, int angle = 1) {
angle %= 4;
if (angle == 0) return grid;
auto h = grid.size(), w = grid[0].size();
auto rotated = std::vector(w, std::vector<T>(h));
for (int y = 0; y < h; y++) for (int x = 0; x < w; x++) rotated[w - 1 - x][y] = grid[y][x];
return rotate(rotated, angle - 1);
}
std::string int128_to_str(__int128_t target) {
std::string target_str;
__uint128_t target_tmp = target < 0 ? -target : target;
do {
target_str += '0' + target_tmp % 10;
target_tmp /= 10;
} while (target_tmp != 0);
if (target < 0) target_str += '-';
std::reverse(target_str.begin(), target_str.end());
return target_str;
}
template <typename T> std::string to_pretty_str(T target) {
using namespace std;
string str;
if constexpr (is_void_v<T>) str += "void"s;
else if constexpr (is_null_pointer_v<T>) str += "null"s;
else if constexpr (is_same_v<T, bool>) str += target ? "true"s : "false"s;
else if constexpr (is_same_v<T, char> || is_same_v<T, char16_t> || is_same_v<T, char32_t> || is_same_v<T, wchar_t>) {
str += "'"s + target + "'"s;
#ifdef INCLUDED_ACL
} else if constexpr (atcoder::internal::is_modint<T>::value) {
str += to_string(target.val()) + "(mod)"s;
#endif // INCLUDED_ACL
} else if constexpr (is_arithmetic_v<T>) {
if constexpr (is_same_v<T, __int128_t>) str += int128_to_str(target);
else str += to_string(target);
if constexpr (is_unsigned_v<T>) str += "u"s;
if constexpr (is_same_v<remove_cv_t<T>, long>) str += "L"s;
else if constexpr (is_same_v<remove_cv_t<T>, long long>) str += "LL"s;
else if constexpr (is_same_v<T, __int128_t>) str += "LLL"s;
} else if constexpr (is_pair_v<T>) {
str += "("s + to_pretty_str(target.first);
str += ", "s + to_pretty_str(target.second) + ")"s;
} else if constexpr (is_convertible_v<T, string>) {
str += "\""s + target + "\""s;
} else if constexpr (is_array_v<T>) {
str += "["s;
bool separate = false;
for (const auto &target_i : target) {
if (separate) str += ", "s;
str += to_pretty_str(target_i);
separate = true;
}
str += "]"s;
} else if constexpr (iterable_v<T>) {
str += "("s + get_typename<T>(20) + "){"s;
bool separate = false;
for (const auto &target_i : target) {
if (separate) str += ","s;
str += " "s + to_pretty_str(target_i);
separate = true;
}
if (separate) str += " "s;
str += "}"s;
} else {
str += "<"s + get_typename<T>(20);
str += " ("s + to_string(sizeof(target)) + " byte)>"s;
}
return str;
}
// input
#ifdef DEBUG
std::chrono::milliseconds input_total_ms{0};
#endif // DEBUG
template <typename T> inline void read_stdin(T &&target) {
#ifdef DEBUG
using namespace std::chrono;
const auto start = system_clock::now();
std::cin >> target;
const auto end = system_clock::now();
input_total_ms += duration_cast<milliseconds>(end - start);
#else // DEBUG
std::cin >> target;
#endif // DEBUG
}
template <typename T> inline T input(T &&target) {
using T_V = std::remove_reference_t<T>;
if constexpr (istreamable_v<T_V>) read_stdin(target);
else if constexpr (iterable_v<T_V>) for (auto &&target_i : target) input(target_i);
else if constexpr (is_pair_v<T_V>) {
input(target.first);
input(target.second);
} else if constexpr (std::is_convertible_v<long long, T_V>) {
long long n;
target = input(n);
} else {
#ifdef DEBUG
std::cerr << "[WARN] Type " << get_typename<T_V>()
<< " is invalid, so input is skipped;" << std::endl;
#endif //DEBUG
}
return target;
}
// input and initialize
struct Scanner { template <typename T> inline operator T() const { T target; return input(target); } } scan;
// output
template <typename T> inline void write_stdout(T target, bool flush = false) {
std::cout << target;
if (flush) std::cout << std::flush;
}
template <typename T, typename Sep = char> inline void output(T target, Sep separator = ' ', bool flush = false) {
if constexpr (ostreamable_v<T>) {
write_stdout(target, flush);
} else if constexpr (std::is_convertible<T, __int128_t>::value) {
write_stdout(int128_to_str(target), flush);
# ifdef INCLUDED_ACL
} else if constexpr (atcoder::internal::is_modint<T>::value) {
output(target.val(), separator, flush);
# endif // INCLUDED_ACL
} else if constexpr (iterable_v<T>) {
bool separate = false;
for (const auto target_i : target) {
if (separate) write_stdout(separator);
output(target_i, separator);
separate = true;
}
if (flush) write_stdout("", flush);
} else if constexpr (is_pair_v<T>) {
output(target.first, separator);
write_stdout(separator);
output(target.second, separator, flush);
} else {
write_stdout("<unknown>", flush);
}
}
template <typename T, typename Sep = char> inline void outputln(T target, Sep separator = ' ', bool flush = false) {
output(target, separator);
write_stdout('\n', flush);
}
// debug output
#ifdef DEBUG
std::chrono::milliseconds debug_total_ms{0};
template <typename F> void debug_txt_f(F callback, int line = -1, std::string file = (__FILE__)) {
using namespace std::chrono;
const auto start = system_clock::now();
std::string dump_str = "[DEBUG] ";
if (line >= 0) {
dump_str += "(";
if (file != (__FILE__)) dump_str += file + ":";
dump_str += "L" + std::to_string(line) + ") ";
}
dump_str += callback();
std::cerr << dump_str << std::endl;
const auto end = system_clock::now();
debug_total_ms += duration_cast<milliseconds>(end - start);
}
# define debug_txt(txt) (debug_txt_f([]() { return to_pretty_str(txt); }, (__LINE__), (__FILE__)), true)
template <typename... Types>
void dump_f(std::string labels, std::tuple<Types...> targets_tupl, int line = -1, std::string file = (__FILE__)) {
debug_txt_f([=]() {
std::string txt;
std::apply([labels, &txt](auto... targets) {
int i = 0, label_left = 0;
(([&](auto target) {
const auto label_len = labels.find(',', label_left) - label_left;
const auto label =
std::regex_replace(labels.substr(label_left, label_len),
std::regex("^\\s+|\\s+$"), "");
if (i >= 1) txt += ", ";
txt += label + ": " + to_pretty_str(target);
label_left += label_len + 1;
i++;
})(targets), ...);
txt += ";";
}, targets_tupl);
return txt;
}, line, file);
}
# define dump(...) (dump_f((#__VA_ARGS__), std::make_tuple(__VA_ARGS__), (__LINE__), (__FILE__)), true)
void dump_canvas_f(std::string label, std::vector<std::string> canvas, int line = -1, std::string file = (__FILE__)) {
debug_txt_f([=]() {
int h = canvas.size(), w = canvas[0].size();
std::string txt = label + " (" + std::to_string(h) + " x " + std::to_string(w) + ")\n";
std::string ruler0(w, ' '), ruler1(w, '-');
for (int x = 0; x < w; x += 4) {
auto x_s = std::to_string(x);
for (std::size_t i = 0; i < x_s.size(); i++) ruler0[x - i] = x_s[x_s.size() - i - 1];
ruler1[x] = '+';
}
txt += " |" + ruler0 + "\n---+" + ruler1;
for (int y = 0; y < h; y++) {
std::string ruler = " |";
if (y % 4 == 0) {
auto y_s = std::to_string(y);
for (std::size_t i = 0; i < y_s.size(); i++) ruler[2 - i] = y_s[y_s.size() - i - 1];
ruler[3] = '+';
}
txt += "\n" + ruler + canvas[y];
}
return txt;
}, line, file);
}
# define dump_canvas(canvas) (dump_canvas_f((#canvas), (canvas), (__LINE__), (__FILE__)), true)
// TODO: dump_table
#else // DEBUG
# pragma GCC diagnostic push
# pragma GCC diagnostic ignored "-Wunused-value"
# define debug_txt(...) (false)
# define dump(...) (false)
# define dump_canvas(...) (false)
# pragma GCC diagnostic pop
#endif // DEBUG
/// main
#if !defined(__INCLUDE_LEVEL__) || __INCLUDE_LEVEL__ <= 1
inline std::string cp_main();
int main() {
using namespace std;
# ifdef DEBUG
using namespace std::chrono;
cerr << "[INFO] running in debug mode!" << endl;
const auto start = system_clock::now();
try {
# endif // DEBUG
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(8);
// run!!!
const auto result = cp_main();
if (!result.empty()) write_stdout(result);
# ifdef DEBUG
write_stdout('\n', true);
} catch (exception &e) {
write_stdout('\n', true);
cerr << "[ERROR] " << e.what() << endl;
}
const auto end = system_clock::now();
const auto time_ms = duration_cast<milliseconds>(end - start) - input_total_ms - debug_total_ms;
cerr << "[INFO] finished in " << time_ms.count() << " ms!" << endl;
# endif // DEBUG
return 0;
}
#endif // __INCLUDE_LEVEL__
/// aliases
using i32 = int; using u32 = unsigned int;
using i64 = long long; using u64 = unsigned long long;
using i128 = __int128; using u128 = unsigned __int128;
using f32 = float; using f64 = double; using f80 = long double;
using str = std::string;
template <typename T> using vec = std::vector<T>;
template <typename T, typename Compare = std::less<T>> using p_que = std::priority_queue<T, std::vector<T>, Compare>;
template <typename Key, typename Compare = std::less<Key>> using mset = std::multiset<Key, Compare>;
template <typename Key, typename T, typename Compare = std::less<Key>> using mmap = std::multimap<Key, T, Compare>;
template <typename Key> using u_set = std::unordered_set<Key>;
template <typename Key> using u_mset = std::unordered_multiset<Key>;
template <typename Key, typename T> using u_map = std::unordered_map<Key, T>;
template <typename Key, typename T> using u_mmap = std::unordered_multimap<Key, T>;
#ifdef INCLUDED_BOOST_CPP_INT
using bigint = boost::multiprecision::cpp_int;
#endif // INCLUDED_BOOST_CPP_INT
using namespace std;
#if __cplusplus >= 202002L && __has_include(<ranges>)
namespace rng = std::ranges;
namespace viw = std::ranges::views;
#endif // C++20 && <ranges>
#ifdef INCLUDED_ACL
using namespace atcoder;
#endif // INCLUDED_ACL
#pragma GCC diagnostic push
# pragma GCC diagnostic ignored "-Wunused-variable"
constexpr auto infi = inf<int>();
constexpr auto infl = inf<long long>();
constexpr auto infd = inf<double>();
constexpr auto infld = inf<long double>();
const std::array YN = { "No"s, "Yes"s };
const std::array AB = { "Bob"s, "Alice"s };
const std::array FS = { "Second"s, "First"s };
const std::array TA = { "Aoki"s, "Takahashi"s };
#pragma GCC diagnostic pop
// functions
#define tostr to_string
#define dist distance
#define min_e min_element
#define max_e max_element
#define iota_v iota_view
#define p1 first
#define p2 second
#define has contains
#define eb emplace_back
#define ef emplace_front
#define pb pop_back
#define pf pop_front
// cast
#define bit_width(x) (int(std::bit_width(x)))
// repeat
#define reps(i, l, r) for (std::decay_t<decltype(r)> i##_right = (r), i = (l); i < i##_right; i++)
#define rep(i, n) reps(i, 0, n)
#define rreps(i, l, r) for (std::decay_t<decltype(r)> i##_left = (l), i = (r) - 1; i >= i##_left; i--)
#define rrep(i, n) rreps(i, 0, n)
#define each(for_able) for (auto &&for_able##_i : (for_able))
// iterate
#define all(for_able) (std::begin(for_able)), (std::end(for_able))
#define rev(for_able) (std::rbegin(for_able)), (std::rend(for_able))
// lambda
#define pred(x, expr) ([&](auto &&x) -> bool { return (expr); })
#define comp(x, y, expr) ([&](auto &&x, auto &&y) -> bool { return (expr); })
/// answer
//using mint=modint998244353;
inline str cp_main() {
i64 x=scan;
if(x==1) {
outputln("2\n1 2\nb g");
return "";
}
vec<pair<vec<int>,bool>> g;
int b=-1;
for(auto [p,e]:factors(x)) {
rep(i,e) {
g.eb(vec<int>{},false);
if(b>=0) {
g[b].p1.eb(ssize(g)-1);
g.back().p1.eb(b);
}
b=ssize(g)-1;
rep(k,p==2&&i<e-1?4:p) {
g[b].p1.eb(ssize(g));
g.eb(vec<int>{b},true);
if(ssize(g)>200000)return "-1\n";
}
if(p==2)++i;
}
}
if(ssize(g)>200000)return "-1\n";
outputln(ssize(g));
rep(i,ssize(g)) {
for(auto k:g[i].p1) {
if(i<k) outputln(pair{i+1,k+1});
}
}
vec<char> c;
rep(i,ssize(g)) c.eb(g[i].p2?'g':'b');
outputln(c);
return "";
}