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Codeforces Round 856 (Div. 2)/D. Counting Factorizations.cpp

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+/* Problem URL: https://codeforces.com/problemset/problem/1794/D */
+
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+
+using namespace std;
+using namespace __gnu_pbds;
+
+template <class T, class comp = less<>>
+using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (int i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (int 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;
+}
+
+const int oo = INT32_MAX >> 1;
+const ll OO = INT64_MAX >> 1;
+
+const ll mod = 998244353;
+
+constexpr MAXN = 1e6 + 10;
+bool prime[MAXN];
+bool vis[MAXN];
+
+vl fact[MAXN];
+vl inv[MAXN];
+
+
+void pre()
+{
+    fill(prime, prime + MAXN, true);
+    prime[0] = false;
+    prime[1] = false;
+
+    nrep(i, 2, MAXN) {
+        if (!prime[i]) {
+            continue;
+        }
+
+        for (int j = i * 2; j < MAXN; j += i) {
+            prime[j] = false;
+        }
+    }
+
+    fact[0] = 1;
+    fact[1] = 1;
+    nrep(i, 2, MAXN) {
+        fact[i] = fact[i - 1] * i % mod;
+    }
+
+    inv[0] = 1;
+    inv[1] = 1;
+    nrep(i, 2, MAXN) {
+        inv[i] = (mod - mod / i) * inv[mod % i] % mod;
+    }
+
+    nrep(i, 2, MAXN) {
+        inv[i] = inv[i - 1] * inv[i] % mod;
+    }
+}
+
+#define TEST 1
+
+void solve()
+{
+    int n;
+    cin >> n;
+
+    vi act(n << 1);
+    cin >> act;
+
+    set<int> up;
+
+    vi ot;
+    vi primes;
+
+    rep(i, n << 1) {
+        if (prime[act[i]]) {
+            if (vis[act[i]]) {
+                ot.push_back(act[i]);
+            } else {
+                up.insert(act[i]);
+                vis[act[i]] = true;
+                primes.push_back(act[i]);
+            }
+            continue;
+        }
+
+        ot.push_back(act[i]);
+    }
+
+    if (primes.size() < n) {
+        cout << "0\n";
+        return;
+    }
+
+    auto comb = [&](int n, int k) {
+        return fact[n] * inv[k] % mod * inv[n - k] % mod;
+    };
+
+    ll ans = comb(primes.size(), n);
+
+    if (ot.empty()) {
+        cout << ans << '\n';
+        return;
+    }
+
+    sortv(ot);
+
+    int c = 1;
+    vi tmp;
+
+    nrep(i, 1, ot.size()) {
+        if (ot[i] == ot[i - 1]) {
+            c++;
+            continue;
+        }
+
+        tmp.push_back(c);
+        c = 1;
+    }
+    tmp.push_back(c);
+
+
+
+    repv(i, up) {
+        vis[i] = false;
+    }
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    pre();
+
+    int t;
+    (TEST && cin >> t) || (t = 1);
+    while (t--) {
+        solve();
+    }
+}