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).