#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; template vector divisors(T x) { vector res1, res2; T d = 1; for(; d * d < x; d++) { if (x % d == 0) { res1.emplace_back(d); res2.emplace_back(x / d); } } if (d * d == x) res1.emplace_back(d); res1.insert(res1.end(), res2.rbegin(), res2.rend()); return res1; } template vector> factorize(T x) { vector> res; for(T p = 2; p * p <= x; p++) { int cnt = 0; while(x % p == 0) x /= p, cnt++; if (cnt) res.emplace_back(p, cnt); } if (x > 1) res.emplace_back(x, 1); return res; } } int main() { ios::sync_with_stdio(false); cin.tie(0); ll n; cin >> n; auto divs = divisors(n); auto fs = factorize(n); int dsz = divs.size(); int fsz = fs.size(); VI idx(dsz); rep(i, dsz) { int now = 0; ll v = divs[i]; rep(j, fsz) { now *= fs[j].second + 1; while(v % fs[j].first == 0) { v /= fs[j].first; now++; } } idx[now] = i; } vector dp(dsz); dp[0] = 1; rep(i, dsz - 1) { VI e(fsz); ll v = divs[i]; rep(j, fsz) { while(v % fs[j].first == 0) { v /= fs[j].first; e[j]++; } } auto dfs = [&](auto&& self, int p, int now, mint c) -> void { if (p == fsz) { dp[idx[now]] += c; return; } now *= fs[p].second + 1; self(self, p + 1, now + e[p], c * mint::raw(e[p] + 1)); for(int i = e[p] + 1; i <= fs[p].second; i++) { self(self, p + 1, now + i, c); } }; dfs(dfs, 0, 0, dp[i]); } mint ans = dp.back(); cout << ans.val() << '\n'; }