2025-09-12 14:50:25 -03:00

159 lines
3.2 KiB
C++

/* Problem URL: https://codeforces.com/problemset/problem/1165/D */
/* what? */
#include <bits/stdc++.h>
using namespace std;
#define V vector
#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)
#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)
#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;
template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
os << vec[0];
for (size_t i = 1; i < vec.size(); i++) {
os << ' ' << vec[i];
}
os << '\n';
return os;
}
template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
for (auto &i : vec) {
is >> i;
}
return is;
}
template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
for (auto &i : vec) {
os << i[0];
for (size_t j = 1; j < i.size(); j++) {
os << ' ' << i[j];
}
os << '\n';
}
return os;
}
template<class v>
auto operator>>(istream &is, vector<vector<v>> &vec)->istream& {
for (auto &i : vec) {
for (auto &j : i) {
is >> j;
}
}
return is;
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
vi check(1e6 + 1);
for (size_t i = 1; i <= 1e6; i++) {
check[i] = i;
}
check[1] = 0;
vi primes;
for (size_t i = 2; i <= 1e6; i++) {
if (check[i] != i) {
continue;
}
primes.push_back(i);
for (size_t j = i * 2; j <= 1e6; j += i) {
check[j] = i;
}
}
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
if (n == 1) {
ll num;
cin >> num;
if (check[num] != num) {
cout << "-1\n";
continue;
}
cout << num * num << '\n';
continue;
}
vl nums(n);
cin >> nums;
sortv(nums);
ll num = nums.back() * nums.front();
ll ans = num;
bool pos = true;
for (auto i : nums) {
if (num % i != 0) {
pos = false;
break;
}
}
if (!pos) {
cout << "-1\n";
continue;
}
int count = 1;
for (size_t i = 0; primes[i] * primes[i] * primes[i] <= num; i++) {
int c = 0;
while (num % primes[i] == 0) {
c++;
num /= primes[i];
}
count *= c + 1;
}
if (check[num] == num) {
count *= 2;
} else if (floor(sqrt(num)) * floor(sqrt(num)) == num && check[sqrt(num)] == floor(sqrt(num))) {
count *= 3;
} else if (num != 1) {
count *= 4;
}
cout << (count - 2 == nums.size() ? ans : -1) << '\n';
}
}