题目

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define fi first
#define se second
#define lson p << 1
#define rson p << 1 | 1
const int maxn = 1e6 + 5, inf = 1e9, maxm = 4e4 + 5;
const int N = 1e6;
 const int mod = 1e9 + 7;
// const int mod = 998244353;
//const __int128 mod = 212370440130137957LL;
// int a[505][5005];
// bool vis[505][505];
int a[maxn], b[maxn];
bool vis[maxn];
string s;
int n, m;

struct Node{
    int val, id;
    bool operator<(const Node &u)const{
        return val < u.val;
    }
};
// Node c[maxn];
struct Rat{
    __int128 a, b;
    bool operator<(const Rat &u)const{
        return a * u.b < u.a * b;
    }
    Rat operator*(const Rat &u)const{
        __int128 up = a * u.a, down = b * u.b;
        __int128 g = __gcd(up, down);
        up /= g, down /= g;
        return Rat({up, down});
    }
};

int ans[maxn];
int pre[maxn];

__int128 qpow(__int128 a, __int128 b){
	__int128 res = 1;
	while(b){
		if(b & 1) res = res * a;
		a = a * a;
		b >>= 1;
	}
	return res;
}

vector<Rat> S;
int calc(__int128 u, __int128 d){
    int cnt = 0;
    for(auto [a, b] : S){
        bool flag = 0;
        for(int i = 1; i <= 63; i++){
            if(qpow(u, i) > a || qpow(d, i) > b){
                return inf;
            }
//             cout << (int)qpow(u, i) << ' ' << (int)a << ' ' << (int)qpow(d, i) << ' ' << (int)b << '\n'; 
            if(qpow(u, i) == a && qpow(d, i) == b){
                flag = 1;
                cnt += i - 1;
                break;
            }
        }
        if(!flag){
            return inf;
        }
    }
    return cnt;
}

//long long ? maxn ?
void solve(){
    int res = 0;
//     int q, k;
    cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
	}
	sort(a + 1, a + n + 1);
	if(a[1] == a[n]){
		cout << n << '\n';
		return;
	}
	n = unique(a + 1, a + n + 1) - a - 1;
	for(int i = 2; i <= n; i++){
        int g = __gcd(a[i], a[i - 1]);
        Rat u = {a[i] / g, a[i - 1] / g};
		S.pb(u);
	}
	res = inf;
    sort(S.begin(), S.end());
    __int128 gu = S.begin() -> a, gd = S.begin() -> b;

    int tmp;
    for(int i = 1; i <= 63; i++){
        __int128 u = pow(gu, 1.0 / i) + 0.5;//加0.5，四舍五入才能过！！！！！！！！！！！！！！！
        __int128 d = pow(gd, 1.0 / i) + 0.5;
        if(qpow(u, i) != gu || qpow(d, i) != gd){
            continue;
        }
        tmp = calc(u, d);
        res = min(res, tmp + n);
    }
    cout << res << '\n';
}
    
signed main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    
    int T = 1;
//    cin >> T;
    while (T--)
    {
        solve();
    }
    return 0;
}