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