#include using namespace std; using ll = long long; #ifdef MY_DEBUG #define dbg(...) debug_out(__VA_ARGS__) #define dbgn(var) debug_out(#var, "=", var) #else #define dbg(...) #define dbgn(...) #endif void debug_out(); template void debug_out(Head, Tail...); template bool chmax(T&, const T&); template bool chmin(T&, const T&); template T pwr(T, ll); template T squ(T x) { return x * x; } ll fact(ll); ll comb(ll, ll); ll ctoll(char); char lltoc(ll); bool flg(ll b, ll i) { return ((b) >> (i)) & 1LL; } // flg(0b010, 1LL) -> true const ll LINF = (ll)1e18 + 7; const double EPS = 1e-9; const int MAX_DUBUG_SIZE = 10; #include #include using namespace atcoder; // const int MOD = 1e9 + 7; // using mint = modint1000000007; const int MOD = 998244353; using mint = modint998244353; // using mint = modint; // main の最初で mint::setmod(/* 任意のMOD */); ostream& operator<<(ostream& os, const mint& N) { return os << N.val(); } // 計算量 O(√N) vector divisor(ll N) { vector res; for (ll i = 1; i * i <= N; ++i) { if (N % i == 0) { res.push_back(i); // 重複しないならば i の相方である N/i も push if (N / i != i) res.push_back(N / i); } } // 小さい順に並び替える sort(res.begin(), res.end()); return res; } // 素因数分解 計算量O(√N) map prime_factor(ll N) { map res; for (ll i = 2; i * i <= N; i++) { while (N % i == 0) { res[i]++; N /= i; } } if (N != 1) { // N が素数の場合 res[N] = 1; } return res; } vector> prime_factor_vector(ll N) { vector> res; for (ll i = 2; i * i <= N; i++) { ll cnt = 0; while (N % i == 0) { cnt++; N /= i; } if (cnt > 0) res.push_back({i, cnt}); } if (N > 1) { // N が素数の場合 res.push_back({N, 1}); } return res; } void solve([[maybe_unused]] int test) { ll n; cin >> n; vector divs = divisor(n); auto pf_n = prime_factor(n); vector>>> divs_pf; for (auto&& x : divs) { auto pf = prime_factor(x); vector> pf_x; for (auto&& [p, q] : pf_n) { pf_x.push_back({p, pf[p]}); } divs_pf.push_back({x, pf_x}); } ll sz = divs.size(); vector dp(sz, 0); dp[0] = 1; for (ll i = 0; i < sz; i++) { auto [x, pf_x] = divs_pf[i]; for (ll j = i + 1; j < sz; j++) { auto [y, pf_y] = divs_pf[j]; if (y % x != 0) continue; mint tmp = dp[i]; for (ll k = 0; k < pf_n.size(); k++) { if (pf_y[k].second == 0) continue; if (pf_x[k].second == pf_y[k].second) { tmp *= pf_y[k].second + 1; } } dp[j] += tmp; } } cout << dp[sz - 1] << "\n"; } int main() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(12); int testcase_size = 1; // cin >> testcase_size; for (int _t = 0; _t < testcase_size; _t++) { solve(_t); } } /* -----------------------------------MY_FUNCTIONS------------------------------------ */ template ostream& operator<<(ostream& os, const pair& pp) { return os << "{" << pp.first << "," << pp.second << "}"; } template ostream& operator<<(ostream& os, const vector& V) { if (V.empty()) return os << "[]"; os << "["; for (ll i = 0; i < (ll)V.size(); i++) { os << V[i] << (i == int(V.size() - 1) ? "]" : ","); } return os; } template ostream& operator<<(ostream& os, const vector>& VV) { if (VV.empty()) return os << "[[]]"; os << "[\n"; for (auto&& V : VV) { os << V << "\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const vector>>& VVV) { if (VVV.empty()) return os << "[[[]]]"; os << "[" << "\n"; int cnt = 0; for (auto&& VV : VVV) { os << cnt++ << VV << "\n\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const set& SS) { if (SS.empty()) return os << "[]"; os << "["; auto ii = SS.begin(); for (; ii != SS.end(); ii++) os << *ii << (ii == prev(SS.end()) ? "]" : ","); return os; } template ostream& operator<<(ostream& os, const map& MM) { if (MM.empty()) return os << "[{:}]"; os << "["; auto ii = MM.begin(); for (; ii != MM.end(); ii++) os << "{" << ii->first << ":" << ii->second << "}" << (ii == prev(MM.end()) ? "]" : ","); return os; } void debug_out() { cerr << endl; } void debug_out_vl(vector V) { const int MAX_SIZE = min((int)V.size(), MAX_DUBUG_SIZE); cerr << "\033[33m"; if (V.empty()) { cerr << "[]" << endl; return; } cerr << "["; for (int i = 0; i < MAX_SIZE; i++) { if (V[i] == LINF) cerr << "INF"; else cerr << V[i]; if (i == (int)V.size() - 1) cerr << "]\n"; else if (i == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } return; } void debug_out_vvl(vector> VV) { cerr << "\033[33m"; if (VV.empty()) { cerr << "[[]]" << endl; return; } cerr << "[\n"; int MAX_ROW = min((int)VV.size(), MAX_DUBUG_SIZE); for (int i = 0; i < MAX_ROW; i++) { const int MAX_COLUMN = min((int)VV[i].size(), MAX_DUBUG_SIZE); if (VV[i].empty()) { cerr << "[]" << endl; continue; } cerr << "["; for (int j = 0; j < MAX_COLUMN; j++) { if (VV[i][j] == LINF) cerr << "INF"; else cerr << VV[i][j]; if (j == (int)VV[i].size() - 1) cerr << "]\n"; else if (j == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } if (i != (int)VV.size() - 1 and i == MAX_DUBUG_SIZE - 1) { cerr << ":\n:\033[m\n"; return; } } cerr << "]\033[m\n"; return; } template void debug_out(Head H, Tail... T) { if constexpr (std::is_same_v>) { debug_out_vl(H); } else if constexpr (std::is_same_v>>) { debug_out_vvl(H); } else { cerr << "\033[33m" << H << "\033[m "; } debug_out(T...); } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template T pwr(T x, ll n) { T res = 1; for (int i = 0; i < n; i++) { res *= x; } return res; } ll fact(ll n) { ll res = 1; for (ll i = 1; i <= n; i++) res *= i; return res; } ll comb(ll n, ll r) { // comb(60, 30)までオーバーフローなし ll res = 1; for (int i = 1; i <= r; i++) { res *= n--; res /= i; } return res; } ll ctoll(char c) { if (c < '0' or '9' < c) { cerr << "\n\033[33m ctoll に '0'~'9' 以外の文字が入りました.\033[m\n" << endl; } return ll(c - '0'); } char lltoc(ll n) { if (n < 0 or 9 < n) { cerr << "\n\033[33m lltoc に 0 ~ 9 以外の数字が入りました.\033[m\n" << endl; } return char(n + '0'); }