From 83c3851438ebbe9c79baf84da345daac974ed114 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Wed, 16 Nov 2022 20:53:58 +0800
Subject: [PATCH] =?UTF-8?q?P4446=20[AHOI2018=E5=88=9D=E4=B8=AD=E7=BB=84]?=
 =?UTF-8?q?=E6=A0=B9=E5=BC=8F=E5=8C=96=E7=AE=80?=
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https://www.luogu.com.cn/record/94275503
---
 Luogu/P4446/P4446.cpp | 68 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 Luogu/P4446/P4446.cpp

diff --git a/Luogu/P4446/P4446.cpp b/Luogu/P4446/P4446.cpp
new file mode 100644
index 00000000..4198ea60
--- /dev/null
+++ b/Luogu/P4446/P4446.cpp
@@ -0,0 +1,68 @@
+#include <iostream>
+#include <cmath>
+#include <unordered_map>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e6 + 5;
+
+int t, p, primes[N];
+bool not_prime[N];
+std::unordered_map<long long, int> map;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    for (int i = 2; i < N; i++) {
+        if (!not_prime[i]) primes[++p] = i;
+
+        for (int j = 1; j <= p && primes[j] * i < N; j++) {
+            not_prime[primes[j] * i] = true;
+
+            if (i % primes[j] == 0) break;
+        }
+    }
+
+    for (int i = 1; i <= p; i++) {
+        long long x = primes[i];
+        map[x * x * x] = primes[i];
+    }
+
+    cin >> t;
+
+    while (t--) {
+        long long n, ans = 1;
+
+        cin >> n;
+
+        int m = std::sqrt(std::sqrt(n));
+
+        if (map.count(n)) {
+            cout << map[n] << endl;
+
+            continue;
+        }
+
+        for (int i = 1, x = primes[i]; i <= p && x <= m && static_cast<long long>(x) * x * x <= n; x = primes[++i]) {
+            long long y = static_cast<long long>(x) * x * x;
+
+            while (n % y == 0) {
+                ans *= x;
+                n /= y;
+            }
+
+            while (n % x == 0) {
+                n /= x;
+            }
+        }
+
+        if (map.count(n)) ans *= map[n];
+
+        cout << ans << endl;
+    }
+
+    return 0;
+}