#include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using pll = pair; using uint = unsigned; using pii = pair; template using pq = priority_queue, greater>; const int IINF = 0x1fffffff; const ll LINF = 0x1fffffffffffffff; const ll MINF = 0x7fffffffffff; const ll MOD = 1000000007; const ll MODD = 998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1}; const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1}; #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll i=0;i(a);) #define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each1(i,a) for(auto&&i:a) #define each2(x,y,a) for(auto&&[x,y]:a) #define each3(x,y,z,a) for(auto&&[x,y,z]:a) #define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) (i).rbegin(),(i).rend() #define rall2(i,k) (i).rbegin(),(i).rbegin()+k #define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) #define dsum(...) accumulate(all(__VA_ARGS__),0.0L) #define Msum(...) accumulate(all(__VA_ARGS__),0_M) #define elif else if #define unless(a) if(!(a)) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define vec vector #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } inline ll popcnt(ull a){ return __builtin_popcountll(a); } ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } template bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; } template bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; } template bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; } template bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; } vector iota(ll n, ll begin = 0){ vector a(n); iota(a.begin(), a.end(), begin); return a; } vector factor(ull x){ vector ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } map factor_map(ull x){ map ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; } vector divisor(ull x){ vector ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } template unordered_map press(vector a){ Uniq(a); unordered_map ans; rep(a.size()) ans[a[i]] = i; return ans; } template map press_map(vector a){ Uniq(a); map ans; rep(a.size()) ans[a[i]] = i; return ans; } int scan(){ return getchar(); } void scan(int& a){ scanf("%d", &a); } void scan(unsigned& a){ scanf("%u", &a); } void scan(long& a){ scanf("%ld", &a); } void scan(long long& a){ scanf("%lld", &a); } void scan(unsigned long long& a){ scanf("%llu", &a); } void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); } void scan(float& a){ scanf("%f", &a); } void scan(double& a){ scanf("%lf", &a); } void scan(long double& a){ scanf("%Lf", &a); } void scan(vector& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto&& i : a) scan(i); } template void scan(deque& a){ for(auto&& i : a) scan(i); } template void scan(array& a){ for(auto&& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto&& i : a) scan(i); } template void scan(T& a){ cin >> a; } void in(){} template void in(T&... a){ (void)initializer_list{ (scan(a), 0)... }; } void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(unsigned a){ printf("%u", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(unsigned long long a){ printf("%llu", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(float a){ printf("%.15f", a); } void print(double a){ printf("%.15f", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } template void print(const complex& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); } template void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const pair& p){ print(p.first); putchar(' '); print(p.second); } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } #ifdef DEBUG inline ll __lg(ull x){ return 63 - __builtin_clzll(x); } #define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) void(0) #endif int first(bool i = true){ return out(i?"first":"second"); } int First(bool i = true){ return out(i?"First":"Second"); } int yes(bool i = true){ return out(i?"yes":"no"); } int Yes(bool i = true){ return out(i?"Yes":"No"); } int No(){ return out("No"); } int YES(bool i = true){ return out(i?"YES":"NO"); } int NO(){ return out("NO"); } int Yay(bool i = true){ return out(i?"Yay!":":("); } int possible(bool i = true){ return out(i?"possible":"impossible"); } int Possible(bool i = true){ return out(i?"Possible":"Impossible"); } int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); } void Case(ll i){ printf("Case #%lld: ", i); } #define fi first #define se second #define rng(a) a.begin(), a.end() #define chmax(x, y) (x = max(x, y)) #define chmin(x, y) (x = min(x, y)) // #define uni(x) x.erase(unique(rng(x)),x.end()) // #define snuke srand((unsigned)clock()+(unsigned)time(NULL)); #define pque priority_queue #define removeerase(x) x.erase(remove(rng(x), 0), x.end()); void debug_out() { std::cerr << std::endl; } template void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cout << " :"; debug_out(t...); } // constexpr uint mod = MODD; // struct Modint{ // uint num = 0; // constexpr Modint() noexcept {} // constexpr Modint(const Modint &x) noexcept : num(x.num){} // inline constexpr operator ll() const noexcept { return num; } // inline constexpr Modint& operator+=(Modint x) noexcept { num += x.num; if(num >= mod) num -= mod; return *this; } // inline constexpr Modint& operator++() noexcept { if(num == mod - 1) num = 0; else num++; return *this; } // inline constexpr Modint operator++(int) noexcept { Modint ans(*this); operator++(); return ans; } // inline constexpr Modint operator-() const noexcept { return Modint(0) -= *this; } // inline constexpr Modint& operator-=(Modint x) noexcept { if(num < x.num) num += mod; num -= x.num; return *this; } // inline constexpr Modint& operator--() noexcept { if(num == 0) num = mod - 1; else num--; return *this; } // inline constexpr Modint operator--(int) noexcept { Modint ans(*this); operator--(); return ans; } // inline constexpr Modint& operator*=(Modint x) noexcept { num = ull(num) * x.num % mod; return *this; } // inline constexpr Modint& operator/=(Modint x) noexcept { return operator*=(x.inv()); } // template constexpr Modint(T x) noexcept { // using U = typename conditional= 4, T, int>::type; // U y = x; y %= U(mod); if(y < 0) y += mod; num = uint(y); // } // template inline constexpr Modint operator+(T x) const noexcept { return Modint(*this) += x; } // template inline constexpr Modint& operator+=(T x) noexcept { return operator+=(Modint(x)); } // template inline constexpr Modint operator-(T x) const noexcept { return Modint(*this) -= x; } // template inline constexpr Modint& operator-=(T x) noexcept { return operator-=(Modint(x)); } // template inline constexpr Modint operator*(T x) const noexcept { return Modint(*this) *= x; } // template inline constexpr Modint& operator*=(T x) noexcept { return operator*=(Modint(x)); } // template inline constexpr Modint operator/(T x) const noexcept { return Modint(*this) /= x; } // template inline constexpr Modint& operator/=(T x) noexcept { return operator/=(Modint(x)); } // inline constexpr Modint inv() const noexcept { ll x = 0, y = 0; extgcd(num, mod, x, y); return x; } // static inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y) noexcept { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } // inline constexpr Modint pow(ull x) const noexcept { Modint ans = 1, cnt = *this; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; } // }; constexpr uint mod = MODD; struct Modint { uint num = 0; constexpr Modint() noexcept {} constexpr Modint(const Modint &x) noexcept : num(x.num) {} inline constexpr operator ll() const noexcept { return num; } inline constexpr Modint& operator+=(Modint x) noexcept {num += x.num; if (num >= mod) num -= mod; return *this; } inline constexpr Modint& operator-=(Modint x) noexcept { if (num < x.num) num += mod; num -= x.num; return *this; } inline constexpr Modint& operator*=(Modint x) noexcept { num = ull(num) * x.num % mod; return *this; } inline constexpr Modint& operator/=(Modint x) noexcept { return operator*=(x.inv()); } inline constexpr Modint& operator++() noexcept { if(num == mod - 1) num = 0; else num++; return *this; } inline constexpr Modint operator++(int) noexcept { Modint ans(*this); operator++(); return ans; } inline constexpr Modint& operator--() noexcept { if(num == 0) num = mod - 1; else num--; return *this; } inline constexpr Modint operator--(int) noexcept { Modint ans(*this); operator--(); return ans; } inline constexpr Modint operator-() const noexcept { return Modint(0) -= *this; } template constexpr Modint(T x) noexcept { using U = typename conditional= 4, T, int>::type; U y = x; y %= U(mod); if(y < 0) y += mod; num = uint(y); } template inline constexpr Modint operator+(T x) const noexcept { return Modint(*this) += x; } template inline constexpr Modint& operator+=(T x) noexcept { return operator+=(Modint(x)); } template inline constexpr Modint operator-(T x) const noexcept { return Modint(*this) -= x; } template inline constexpr Modint& operator-=(T x) noexcept { return operator-=(Modint(x)); } template inline constexpr Modint operator*(T x) const noexcept { return Modint(*this) *= x; } template inline constexpr Modint& operator*=(T x) noexcept { return operator*=(Modint(x)); } template inline constexpr Modint operator/(T x) const noexcept { return Modint(*this) /= x; } template inline constexpr Modint& operator/=(T x) noexcept { return operator/=(Modint(x)); } inline constexpr Modint inv() const noexcept { ll x = 0, y = 0; extgcd(num, mod, x, y); return x; } static inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y) noexcept { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } inline constexpr Modint pow(ull x) const noexcept { Modint ans = 1, cnt = *this; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; } }; std::istream& operator>>(std::istream& is, Modint& x){ ll a; in(a); x = a; return is; } inline constexpr Modint operator""_M(ull x) noexcept { return Modint(x); } std::vector fac(1, 1), inv(1, 1); inline void reserve(ll a){ if(fac.size() >= a) return; if(a < fac.size() * 2) a = fac.size() * 2; if(a >= mod) a = mod; while(fac.size() < a) fac.push_back(fac.back() * Modint(fac.size())); inv.resize(fac.size()); inv.back() = fac.back().inv(); for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i; } inline Modint fact(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; } inline Modint perm(ll n, ll r){ if(r < 0 || n < r) return 0; if(n >> 24){ Modint ans = 1; for(ll i = 0; i < r; i++) ans *= n--; return ans; } reserve(n + 1); return fac[n] * inv[n - r]; } inline Modint comb(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(r + 1); return perm(n, r) * inv[r]; } inline Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // r balls into n boxes inline Modint catalan(ll n){ reserve(n * 2 + 1); return fac[n * 2] * inv[n] * inv[n + 1]; } ll gcd(ll a, ll b) { if (b) return gcd(b, a % b); return a; } ll lcm(ll a, ll b) { return a * b / gcd(a, b); } ll extgcd(ll a, ll b, ll &x, ll &y) { ll g = a; x = 1; y = 0; if (b) { g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } vector primes(ll n) { vec primes(n); for (ll i = 2; i < n; ++i) primes[i] = i; for (ll i = 2; i * i < n; ++i) { if (primes[i]) for (ll j = i * i; j < n; j += i) primes[j] = 0; } auto p = remove(primes.begin(), primes.end(), 0); primes.erase(p, primes.end()); return primes; } // vector facmod; // vector facinvmod; // ll combination(ll n, ll k, ll mod) { // // 階乗やその逆元をメモ化すると速い // // でかいやつはnCk/2^Nをパスカルの三角形で作る // ll res = fac(n, mod); // res = (res * invmod(fac(k, mod), mod)) % mod; // res = (res * invmod(fac(n - k, mod), mod)) % mod; // return res; // } // x % m[i] = r[i] % m[i] を満たす正で最小の x を返す // i!=j に対して gcd(m[i], m[j])=1 であると仮定 // とりあえず解の存在判定は保留 // ll garner(vector r, vector m) { // int n = r.size(); // ll m_prod = 1; // m_prod には m[i] の積を入れていく // ll x = r[0] % m[0]; // 最初の条件を満たすような x の初期値 // for (int i = 1; i < n; i++) { // // cout << r[i-1] << " " << m[i-1] << " " << x << endl; // m_prod *= m[i - 1]; // m の累積積を更新 // ll t = ((r[i] - x) * invmod(m_prod, m[i])) % m[i]; // if (t < 0) // t += m[i]; // x += t * m_prod; // x を更新 // } // return x; // } // false: composite, true: probably prime // bool MillarRabin_sub(ll n, ll random) { // ll d = n-1; // while(d % 2 == 0) { // // d /= 2; // cout << random << " " << powmod(random, d, n) << endl; // if (powmod(random, d, n) == n-1) { // return true; // } // } // if (powmod(random, d, n) == 1) return true; // return false; // } // bool MillarRabin(ll n) { // random_device rd{}; // vector vec(20); // generate(vec.begin(), vec.end(), ref(rd)); // mt19937 mt(seed_seq(vec.begin(), vec.end())); // bool ret = true; // rep(i,0,20) { // vec[i] %= n; if (vec[i] == 0) continue; // cout << MillarRabin_sub(n, random) << endl; // if (!MillarRabin_sub(n, random)) return false; // } // return true; // } // 逆順になる reverse(rng(ans)); // vector G[100000]; // cout << fixed << setprecision(15) << y << endl; // cout << bitset<20>(i) << endl; // fill(distance[0], distance[row], INF); // __builtin_popcount() // stoi(S[j], 0, 2) // for (ll i = 0;i < (ll)s.size() - k;i++) // ll dp[桁数][未満フラグ][条件を満たしているか] // stoi stoll // bit全探索 n進数全探索 // while (t > 0) cc += t % 9, t /= 9; // priority_queue que; que.push(3); que.top(); que.pop(); // rep(i,C)rep(j,C) if(i != j) rep(k,C) if(i != k && j != k) // 始点終点をデータに含ませる // memory restriction RE -> CE // forr 逆順ループsnippet // 座標 上下の回数さえ分かれば組合せ問題 // set 順序付き集合 distance(set.begin(), itr)でオフセットがわかる // set s : for(int x : s) for(int y : s) for(int z : s) // const int di[4] = {-1, 0, 1, 0}; // const int dj[4] = {0, -1, 0, 1}; // const string let = "ULDR"; // 逆順ソートsort(cand.rbegin(), cand.rend()); // int ok = 0, ng = 1e9+1; // auto check = [&](int x) -> bool { // set s; // rep(i,0,N) { // int tmp = 0; // rep(j,0,5) { // if (A[i][j] >= x) tmp |= 1 << j; // } // s.insert(tmp); // } // for (int x : s) for (int y : s) for (int z : s) { // if ((x | y | z) == 31) return true; // } // return false; // }; // while(abs(ok - ng) > 1) { // int mid = (ok + ng) / 2; // if (check(mid)) ok = mid; // else ng = mid; // } // cout << ok << endl; // dp[500][500] はllではなくintにすること // chmin/chmaxは型をあわせないといけない // priority_queue 最上位以外アクセス許可していない // priority_queue, greater> // multiset イテレータ書き込み出来ない int main() { ios::sync_with_stdio(false); cin.tie(nullptr); LL(n); Modint ans = 1; each(p, primes(n)) { ll mx = 0; rep(i,p,n+1,p) { ll x = i, y = n-i, cnt = 0; while(x % p == 0) { x /= p; cnt++; } while(y % p == 0) { y /= p; cnt++; } chmax(mx, cnt); } ans *= Modint(p).pow(mx); } cout << ans << endl; return 0; }