結果

問題 No.314 ケンケンパ
ユーザー raven7959
提出日時 2024-01-12 12:41:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 93 ms / 1,000 ms
コード長 32,395 bytes
コンパイル時間 3,059 ms
コンパイル使用メモリ 225,484 KB
最終ジャッジ日時 2025-02-18 17:28:31
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 17
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
/*
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")
*/
#define rep(i, n) for (ll i = 0; i < (int)(n); i++)
#define rrep(i, n) for (ll i = (int)(n) - 1; i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) ll(x.size())
#define yn(joken) cout<<((joken) ? "Yes" : "No")<<"\n"
#define YN(joken) cout<<((joken) ? "YES" : "NO")<<"\n"
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vpi = vector<pair<int,int>>;
using vpl = vector<pair<ll,ll>>;
using vs = vector<string>;
using vc = vector<char>;
using vd = vector<double>;
using vld = vector<long double>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;
using vvs = vector<vector<string>>;
using vvc = vector<vector<char>>;
using vvd = vector<vector<double>>;
using vvld = vector<vector<long double>>;
using vvvi = vector<vector<vector<int>>>;
using vvvl = vector<vector<vector<ll>>>;
using vvvvi = vector<vector<vector<vector<int>>>>;
using vvvvl = vector<vector<vector<vector<ll>>>>;
template <class T> using priq = priority_queue<T>;
template <class T> using priqg = priority_queue<T, vector<T>, greater<T>>;
const int INF = 1e9;
const ll LINF = 2e18;
template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
template <typename T>
vi iota(int n) {
    vi a(n);
    return iota(a.begin(), a.end(), 0), a;
}
template <typename T> vi iota(const vector<T> &a, bool greater = false) {
    vi ret(a.size());
    iota(ret.begin(), ret.end(), 0);
    sort(ret.begin(), ret.end(), [&](int i, int j) {
        if(greater) return a[i] > a[j];
        return a[i] < a[j];
    });
    return ret;
}
template <typename S> void rearrange(const vector<S> &id) {}
template <typename S, typename T> void rearrange_exec(const vector<S> &id, vector<T> &v) {
    vector<T> w(v.size());
    rep(i, sz(id)) w[i] = v[id[i]];
    v.swap(w);
}
// 並び替える順番, 並び替えるvector
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S> &id, Head &a, Tail &...tail) {
    rearrange_exec(id, a);
    rearrange(id, tail...);
}
template <typename T> vector<T> RUI(const vector<T> &v) {
    vector<T> res(v.size() + 1);
    for(int i = 0; i < v.size(); i++) res[i + 1] = res[i] + v[i];
    return res;
}
// 反時計周りに 90 度回転
template <typename T> void roth(vector<vector<T>> &v) {
    if(empty(v)) return;
    int n = v.size(), m = v[0].size();
    vector<vector<T>> res(m, vector<T>(n));
    rep(i, n) rep(j, m) res[m - 1 - j][i] = v[i][j];
    v.swap(res);
}
// 時計周りに 90 度回転
template <typename T> void rott(vector<vector<T>> &v) {
    if(empty(v)) return;
    int n = v.size(), m = v[0].size();
    vector<vector<T>> res(m, vector<T>(n));
    rep(i, n) rep(j, m) res[j][n - 1 - i] = v[i][j];
    v.swap(res);
}
bool ispow2(int i) { return i && (i & -i) == i; }
bool ispow2(ll i) { return i && (i & -i) == i; }
template <typename T, typename S> T ceil(T x, S y) { // x/y以上の最小の整数を返す
    assert(y);
    return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
 
template <typename T, typename S> T floor(T x, S y) { // x/y以下の最大の整数を返す
    assert(y);
    return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
template <class S> vector<pair<S, int>> RunLength(const vector<S> &v) {
    vector<pair<S, int>> res;
    for(auto &e : v) {
        if(res.empty() || res.back().first != e)
            res.emplace_back(e, 1);
        else
            res.back().second++;
    }
    return res;
}
vector<pair<char, int>> RunLength(const string &v) {
    vector<pair<char, int>> res;
    for(auto &e : v) {
        if(res.empty() || res.back().first != e)
            res.emplace_back(e, 1);
        else
            res.back().second++;
    }
    return res;
}
template <class T, class F> T bin_search(T ok, T ng, const F &f) {
    while(abs(ok - ng) > 1) {
        T mid = ok + ng >> 1;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class T, class F> T bin_search_double(T ok, T ng, const F &f, int iter = 80) {
    while(iter--) {
        T mid = (ok + ng) / 2;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        is >> v[i];
    }
    return is;
}
namespace aux {
template <typename T, unsigned N, unsigned L> struct tp {
    static void output(std::ostream &os, const T &v) {
        os << std::get<N>(v) << (&os == &cerr ? ", " : " ");
        tp<T, N + 1, L>::output(os, v);
    }
};
template <typename T, unsigned N> struct tp<T, N, N> {
    static void output(std::ostream &os, const T &v) { os << std::get<N>(v); }
};
} // namespace aux
template <typename... Ts> std::ostream &operator<<(std::ostream &os, const std::tuple<Ts...> &t) {
    if(&os == &cerr) { os << '('; }
    aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::output(os, t);
    if(&os == &cerr) { os << ')'; }
    return os;
}
template <typename T> std::ostream &operator<<(std::ostream &os, const stack<T> &_st) {
    auto st = _st;
    vector<T> res;
    while(!empty(st)) res.emplace_back(st.top()), st.pop();
    reverse(all(res));
    return os << res;
}
template <typename T> std::ostream &operator<<(std::ostream &os, const queue<T> &_qu) {
    auto qu = _qu;
    vector<T> res;
    while(!empty(qu)) res.emplace_back(qu.front()), qu.pop();
    return os << res;
}
template <typename T> std::ostream &operator<<(std::ostream &os, const deque<T> &_dq) {
    auto dq = _dq;
    vector<T> res;
    while(!empty(dq)) res.emplace_back(dq.front()), dq.pop_front();
    return os << res;
}
template <typename T, typename S, typename U> std::ostream &operator<<(std::ostream &os, const priority_queue<T, S, U> &_pq) {
    auto pq = _pq;
    vector<T> res;
    while(!empty(pq)) res.emplace_back(pq.top()), pq.pop();
    return os << res;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
    if(&os == &cerr) { return os << "(" << p.first << ", " << p.second << ")"; }
    return os << p.first << " " << p.second;
}
template <class Ch, class Tr, class Container> std::basic_ostream<Ch, Tr> &operator<<(std::basic_ostream<Ch, Tr> &os, const Container &x) {
    bool f = true;
    if(&os == &cerr) os << "[";
    for(auto &y : x) {
        if(&os == &cerr)
            os << (f ? "" : ", ") << y;
        else
            os << (f ? "" : " ") << y;
        f = false;
    }
    if(&os == &cerr) os << "]";
    return os;
}
#pragma region modint
 
#include <algorithm>
#include <array>
 
#ifdef _MSC_VER
#include <intrin.h>
#endif
 
namespace modint {
 
namespace internal {
 
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
 
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}
 
}  // namespace internal
 
}  // namespace modint
 
#include <utility>
 
namespace modint {
 
namespace internal {
 
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
 
// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;
 
    // @param m `1 <= m`
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {
    }
 
    // @return m
    unsigned int umod() const {
        return _m;
    }
 
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay
 
        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1)
        // < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};
 
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
 
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
 
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
 
    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
 
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b
 
        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b
 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}
 
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
 
}  // namespace internal
 
}  // namespace modint
 
#include <cassert>
#include <numeric>
#include <type_traits>
 
namespace modint {
 
namespace internal {
 
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;
 
template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
 
#else
 
template <class T>
using is_integral = typename std::is_integral<T>;
 
template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;
 
template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;
 
#endif
 
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
 
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
 
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
 
}  // namespace internal
 
}  // namespace modint
 
#include <cassert>
#include <numeric>
#include <type_traits>
 
#ifdef _MSC_VER
#include <intrin.h>
#endif
 
namespace modint {
 
namespace internal {
 
struct modint_base {};
struct static_modint_base : modint_base {};
 
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
 
}  // namespace internal
 
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
 
public:
    static constexpr int mod() {
        return m;
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
 
    static_modint() : _v(0) {
    }
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) {
        _v = ((unsigned int)(v) % umod());
    }
 
    unsigned int val() const {
        return _v;
    }
 
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
 
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this = *this * rhs.inv();
    }
 
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
 
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
 
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
 
private:
    unsigned int _v;
    static constexpr unsigned int umod() {
        return m;
    }
    static constexpr bool prime = internal::is_prime<m>;
};
 
template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
 
public:
    static int mod() {
        return (int)(bt.umod());
    }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
 
    dynamic_modint() : _v(0) {
    }
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) {
        _v = ((unsigned int)(v) % mod());
    }
 
    unsigned int val() const {
        return _v;
    }
 
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
 
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this = *this * rhs.inv();
    }
 
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
 
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
 
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
 
private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() {
        return bt.umod();
    }
};
template <int id>
internal::barrett dynamic_modint<id>::bt = 998244353;
 
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
 
namespace internal {
 
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
 
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
 
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
 
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
 
}  // namespace internal
 
}  // namespace modint
 
#include <cassert>
#include <type_traits>
#include <vector>
 
namespace modint {
 
namespace internal {
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
 
    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
 
    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
 
    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}
 
}  // namespace internal
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}
 
template <unsigned int mod = 998244353, class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
 
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}
 
std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
 
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
 
    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;
 
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
 
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
 
    return c;
}
template <typename T, typename std::enable_if_t<internal::is_modint<T>::value,
                                                std::nullptr_t> = nullptr>
std::istream& operator>>(std::istream& is, T& v) {
    long long x;
    is >> x;
    v = x;
    return is;
}
template <typename T, typename std::enable_if_t<internal::is_modint<T>::value,
                                                std::nullptr_t> = nullptr>
std::ostream& operator<<(std::ostream& os, const T& v) {
    os << v.val();
    return os;
}
 
}  // namespace modint
#pragma endregion
using mint = modint::modint1000000007;
// using mint = modint::modint998244353;
// using mint = modint::modint;
/* 任意modの場合
using mint = modint::modint;
-> main内で mint::set_mod(mod);
*/
const long long mod=1000000007;
// const long long mod=998244353;
// long long mod; // あとで受け取る
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
using vvvm = vector<vector<vector<mint>>>;
using vvvvm= vector<vector<vector<vector<mint>>>>;
vector<long long> _fact={1,1};
vector<long long> _inv={1,1};
vector<long long> _finv={1,1};
template<class T>
long long  modinv(T n){
    long long ret=1;
    long long e=mod-2;
    while(e){
        if(e&1){
            ret*=n;
            ret%=mod;
        }
        n=n*n%mod;
        e>>=1;
    }
    return ret;
}
template<class T>
long long modf(T n){
    if(int(_fact.size())>n) return _fact[n];
    for(int i=int(_fact.size());i<=n;i++){
        _fact.push_back(_fact[i-1]*i%mod);
        _inv.push_back(mod-_inv[mod%i]*(mod/i)%mod);
        _finv.push_back(_finv[i-1]*_inv[i]%mod);
    }
    return _fact[n];
}
template<class T>
long long modfinv(T n){
    if(int(_finv.size())>n) return _finv[n];
    modf(n); // modfinvだけ欲しくなって呼び出したときに壊れそうなので
    return _finv[n];
}
template<class T,class U>
long long combination(T n,U k){
    //assert(n>=0 && k>=0);
    if(n<0 || k<0) return 0;
    if(k>n/2) k=n-k;
    if(n<k) return 0;
    if(n==k) return 1;
    if(n>=mod){
        long long ret=1;
        while(n|k){
            ret*=combination(n%mod,k%mod);
            ret%=mod;
            n/=mod;
            k/=mod;
        }
        return ret;
    }
    if(n>3000000){
        long long ret=1;
        for(long long i=0;i<k;i++){
            ret=(n-i)%mod*ret%mod;
        }
        ret=ret*modfinv(k)%mod;
        return ret;
    }
    return modf(n)*modfinv(k)%mod*modfinv(n-k)%mod;
}
static uint32_t RandXor(){
    static uint32_t x=123456789;
    static uint32_t y=362436069;
    static uint32_t z=521288629;
    static uint32_t w=88675123;
    uint32_t t;
 
    t=x^(x<<11);
    x=y; y=z; z=w;
    return w=(w^(w>>19))^(t^(t>>8));
}
static double Rand01(){
    return (RandXor()+0.5)*(1.0/UINT_MAX);
}
void solve(){
    ll N;
    cin>>N;
    vvm dp(N,vm(3));
    dp[0][1]=1;
    rep(i,N-1){
        rep(j,3){
            if(j) dp[i+1][0]+=dp[i][j];
            if(j<2) dp[i+1][j+1]+=dp[i][j];
        }
    }
    cout<<dp[N-1][0]+dp[N-1][1]+dp[N-1][2]<<"\n";
}
int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    solve();
}
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