CF2205B Simons and Cakes for Success

When I succeed, we'll share the cakes together! — SHUN Simons has $ n $ friends and a huge amount of cakes. To divide the cakes fairly, you are asked to help him solve the following problem: - Find the minimum positive integer $ k $ such that $ n $ is a divisor of $ k^n $ . It can be proved that the answer always exists under the given constraints.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). The description of the test cases follows. The only line of each test case contains a single integer $ n $ ( $ 2\le n\le 10^9 $ ) — the number of friends Simons has.

For each test case, output a single integer — the minimum $ k $ you found.

In the first test case: - $ 1^8=1 $ , and $ 8 $ is not a divisor of $ 1 $ ; - $ 2^8=256 $ , and $ 8 $ is a divisor of $ 256 $ , because $ 256 = 8\cdot 32 $ . Thus, the minimum possible $ k $ is $ 2 $ . In the second test case, $ 12 $ is a divisor of $ 6^{12}=2\,176\,782\,336 $ , because $ 2\,176\,782\,336=12\cdot 181\,398\,528 $ .