#include using namespace std; using ll = long long; using pll = pair; #define drep(i, cc, n) for (ll i = (cc); i <= (n); ++i) #define rep(i, n) drep(i, 0, n - 1) #define all(a) (a).begin(), (a).end() #define pb push_back #define fi first #define se second mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count()); const ll MOD1000000007 = 1000000007; const ll MOD998244353 = 998244353; const ll MOD[3] = {999727999, 1070777777, 1000000007}; const ll LINF = 1LL << 60; const int IINF = 1 << 30 - 1; template struct Edge{ int to; T w; Edge(int to_, T w_=1){ to = to_; w=w_; } }; template using Tree = vector>>; template using Graph = vector>>; /* 容量&重み付きエッジ for Dinic */ template struct REdge{ int to; T cap; T cost; int rev; REdge(int to_, T cap_, T cost_=1){ to = to_; cap = cap_; cost = cost_; } REdge(int to_, T cap_, T cost_, int rev_){ to = to_; cap = cap_; cost = cost_; rev = rev_; } }; /* 残余グラフ for Dinic */ template using RGraph = vector>>; template class modint{ long long x; public: modint(long long x=0) : x((x%mod+mod)%mod) {} modint operator-() const { return modint(-x); } bool operator==(const modint& a){ if(x == a) return true; else return false; } bool operator==(long long a){ if(x == a) return true; else return false; } bool operator!=(const modint& a){ if(x != a) return true; else return false; } bool operator!=(long long a){ if(x != a) return true; else return false; } modint& operator+=(const modint& a) { if ((x += a.x) >= mod) x -= mod; return *this; } modint& operator-=(const modint& a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } modint& operator*=(const modint& a) { (x *= a.x) %= mod; return *this; } modint operator+(const modint& a) const { modint res(*this); return res+=a; } modint operator-(const modint& a) const { modint res(*this); return res-=a; } modint operator*(const modint& a) const { modint res(*this); return res*=a; } modint pow(long long t) const { if (!t) return 1; modint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod modint inv() const { return pow(mod-2); } modint& operator/=(const modint& a) { return (*this) *= a.inv(); } modint operator/(const modint& a) const { modint res(*this); return res/=a; } friend std::istream& operator>>(std::istream& is, modint& m) noexcept { is >> m.x; m.x %= mod; if (m.x < 0) m.x += mod; return is; } friend ostream& operator<<(ostream& os, const modint& m){ os << m.x; return os; } }; using mint = modint; int main(){ cin.tie(nullptr); ios::sync_with_stdio(false); ll n; cin >> n; vector div; for(ll i=1; i*i<=n; i++){ if(n%i!=0) continue; div.pb(i); if(i!=n/i) div.pb(n/i); } sort(all(div)); ll m = (ll)div.size(); vector p; ll sn = n; for(ll i=2; i*i<=n; i++){ if(sn%i!=0) continue; while(sn%i==0) sn/=i; p.pb(i); } if(sn!=1) p.pb(sn); ll pn = (ll)p.size(); vector> cnt(m, vector(pn, 0)); rep(i, m){ ll tmp = div[i]; rep(j, pn){ while(tmp%p[j]==0){ tmp/=p[j]; cnt[i][j]++; } } } vector> r(m, vector(m, 1)); rep(i, m) rep(j, m){ if(div[i]%div[j]!=0) continue; //j->i rep(k, pn) if(cnt[i][k]==cnt[j][k]) r[i][j] *= cnt[j][k]+1; } vector> cand(m); rep(i, m) rep(j, m) if(div[i]%div[j]==0 && i!=j) cand[i].pb(j); vector> dp(2, vector(m, 0)); auto crt = dp[0], nxt = dp[1]; crt[0] = 1; mint ans = 0; while(true){ for(ll i=0; i