#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const ll MOD=1e9+7;
ll powmod(ll a, ll k){
    ll ap=a, ans=1;
    while(k){
        if(k&1){
            ans*=ap;
            ans%=MOD;
        }
        ap=ap*ap;
        ap%=MOD;
        k>>=1;
    }
    return ans;
}
ll inv(ll a){
    return powmod(a, MOD-2);
}
ll f[200020], invf[200020];
void fac(int n){
    f[0]=1;
    for(ll i=1; i<=n; i++) f[i]=f[i-1]*i%MOD;
    invf[n]=inv(f[n]);
    for(ll i=n-1; i>=0; i--) invf[i]=invf[i+1]*(i+1)%MOD;
}
ll comb(int x, int y){
    if(!(0<=y && y<=x)) return 0;
    return f[x]*invf[y]%MOD*invf[x-y]%MOD;
}
int main()
{
    int m; cin>>m;
  int m1=m;
    vector<P> fac;
    for(int i=2; i*i<=m; i++){
        if(m%i==0){
            int e=0;
            while(m%i==0){
                m/=i;
                e++;
            }
            fac.push_back({i, e});
        }
    }
    if(m>1) fac.push_back({m, 1});
    ll ans=1;
    for(auto q:fac){
        ll ans1=0;
        int e=q.second, p=q.first;
        auto dfs=[&](auto dfs, int e1, vector<P> &v){
            if(e1==0){
                ll s=1;
                for(int i=0; i<v.size(); i++){
                    int k=v[i].second, n=v[i].first;
                  //cout<<n<<" "<<k<<endl;
                    s*=powmod(p, (ll)(n-1)*k*k);
                    s%=MOD;
                    for(int j=0; j<k; j++){
                        (s*=(powmod(p, k)-powmod(p, j)+MOD))%=MOD;
                    }
                    for(int j=0; j<v.size(); j++){
                        if(i==j) continue;
                        (s*=powmod(p, (ll)min(v[j].first, n)*v[j].second*k))%=MOD;
                    }
                }
              //cout<<endl;
                (ans1+=inv(s))%=MOD;
                return;
            }
            for(int k=1; k<=e1 && (v.empty() || k<v.back().first); k++){
                for(int j=1; j*k<=e1; j++){
                    if(k==1 && j<e1) continue;
                    v.push_back({k, j});
                    dfs(dfs, e1-j*k, v);
                    v.pop_back();
                }
            }
        };
        vector<P> v;
        dfs(dfs, e, v);
        (ans*=ans1)%=MOD;
    }
    for(int i=1; i<=m1; i++) (ans*=i)%=MOD;
    cout<<ans<<endl;
    return 0;
}