void fact(ll n, vl& ret) {
    if(n == 1) return;
    else if(n%2 == 0) ret.pb(2), fact(n/2, ret);
    else if(is_p(n)) ret.pb(n);
    else {
        ll a, b, c, g = n;
        auto f = [&c, &n](ll x)->ll{return (c+(lll)x*x)%n;};
        
        do {
            if(g == n) a=b=rand()%(n-2)+2, c=rand()%20+1;
            a=f(a); b=f(f(b));
            g = gcd(a-b, n);
        } while(g == 1);
        fact(g, ret); fact(n/g, ret);
    }
}
vl po_rho(ll n) {
    vl ret;
    fact(n, ret);
    sort(all(ret));
    return ret;
}