#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } int main() { ll K; cin >> K; vector divs(0); // 約数の個数の 2 乗はおそらくかけていい // これに対応する「A の個数」を別立てで求めてみようか for (ll i = 1; i * i <= K; i++) { if (K % i == 0) { divs.push_back(i); if (i * i != K) { divs.push_back(K / i); } } } sort(all(divs)); ll len = divs.size(); vector dp(len, 0); dp[0] = mint(1); // debug(divs); // 素因数分解してみよう map mp; ll Kcpy = K; for (ll i = 2; i * i <= K; i++) { while (true) { if (Kcpy % i != 0) { break; } mp[i]++; Kcpy /= i; } } if (Kcpy != 1) { mp[Kcpy]++; } // debug(mp); ll len_mp = mp.size(); vector prvec(0); for (auto it = mp.begin(); it != mp.end(); it++) { prvec.push_back(it->first); } // 各約数が何回割れるかテーブルを持ちましょう vector> divs_cnt(len, vector(len_mp, 0)); for (ll i = 0; i < len; i++) { ll div_cpy = divs[i]; for (ll j = 0; j < len_mp; j++) { while (div_cpy % prvec[j] == 0) { div_cpy /= prvec[j]; divs_cnt[i][j]++; } } } // debug(divs_cnt); // いよいよ遷移していこう for (ll i = 0; i < len; i++) { for (ll j = i + 1; j < len; j++) { mint prd = mint(1); for (ll k = 0; k < len_mp; k++) { if (divs_cnt[i][k] > divs_cnt[j][k]) { prd = mint(0); break; } if (divs_cnt[i][k] == divs_cnt[j][k]) { prd *= mint(divs_cnt[i][k] + 1); } } dp[j] += dp[i] * prd; } } // debug_mint1(dp); cout << dp[len - 1].val() << endl; }