#include #include typedef long long int ll; typedef long double ld; using namespace std; using namespace atcoder; #define inf 1010000000 #define llinf 1001000000000000000ll #define pi 3.141592653589793238 #define rep(i, n) for(ll i = 0; i < (n); i++) #define rep1(i, n) for(ll i = 1; i <= (n); i++) #define rep2(i,l,r) for(ll i = (l); i < (r); i++) #define per(i, n) for(ll i = (n)-1; i >= 0; i--) #define each(x, v) for (auto&& x : v) #define rng(a) a.begin(),a.end() #define fi first #define se second #define pb push_back #define eb emplace_back #define pob pop_back #define st string #define sz(x) (int)(x).size() #define mems(x) memset(x, -1, sizeof(x)); #define pcnt __builtin_popcountll #define _GLIBCXX_DEBUG #define dame { puts("-1"); return 0;} #define yes { puts("Yes"); return 0;} #define no { puts("No"); return 0;} #define ret(x) { cout<<(x)< inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false;} template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false;} // 仮マクロ 便利だったら昇格 #define dump(x) { cout << #x << " = " << (x) << endl;} #define bit(n) (1LL<<(n)) #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end()) template inline T in(){ T x; cin >> x; return (x);} #define vcin(x,n) {for(ll loop=0; loop<(n); loop++) cin>>x[loop];} // ここまで仮マクロ // srand((unsigned)time(NULL)); rand()を用いる際にmainの頭に置く // clock()/CLOCKS_PER_SEC 秒数を知りたいときに用いる #define mod 998244353 using mint = modint998244353; /* #define mod 1000000007 using mint = modint1000000007; */ vector dx={1,0,-1,0}; vector dy={0,1,0,-1}; using pl = pair; using ppl = pair; using V = vector; using Graph = vector>; // G.assign(n, vector()); グローバル変数にGを置く時に置く // 関数を置くのはここ以下 // 単純な約数の列挙 vector div(ll k){ vector v; for(ll i=1; i*i<=k; i++){ if(k%i==0){ v.eb(i); if(i*i!=k){ v.eb(k/i); } } } sort(rng(v)); return v; } vector prime(ll k){ vector v; for(ll i=2; i*i<=k; i++){ if(k%i==0){ while(k%i==0){ k /= i; } v.eb(i); if(k==1) break; } } if(k!=1){ v.eb(k); } return v; } vector prime2(ll k){ vector p; for(ll i=2; i*i<=k; i++){ if(k%i==0){ ll tmp = 0; while(k%i==0){ tmp++; k /= i; } p.eb(i,tmp); if(k==1) break; } } if(k!=1){ p.eb(k,1); } return p; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); ll n = in(); vector v = div(n); ll m = v.size(); mint dp[m][m]; // i番目からj番目への遷移 vector> p2(m); rep(i,m){ p2[i] = prime2(v[i]); } rep(i,m){ rep(j,m){ if(i>=j) dp[i][j] = 0; else{ if(v[j]%v[i]!=0){ dp[i][j] = 0; continue; } vector p = prime(v[j]/v[i]); dp[i][j] = 1; each(x,p2[j]){ dp[i][j] *= x.se+1; each(y,p){ if(y==x.fi){ dp[i][j] /= x.se+1; break; } } } } } } mint dp2[m]; dp2[0] = 1; rep(i,m){ rep(j,m){ if(i>j) continue; dp2[j] += dp2[i] * dp[i][j]; } } ret(dp2[m-1].val()) }