CF1855B Longest Divisors Interval

Given a positive integer $ n $ , find the maximum size of an interval $ [l, r] $ of positive integers such that, for every $ i $ in the interval (i.e., $ l \leq i \leq r $ ), $ n $ is a multiple of $ i $ . Given two integers $ l\le r $ , the size of the interval $ [l, r] $ is $ r-l+1 $ (i.e., it coincides with the number of integers belonging to the interval).

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The only line of the description of each test case contains one integer $ n $ ( $ 1 \leq n \leq 10^{18} $ ).

For each test case, print a single integer: the maximum size of a valid interval.

In the first test case, a valid interval with maximum size is $ [1, 1] $ (it's valid because $ n = 1 $ is a multiple of $ 1 $ ) and its size is $ 1 $ . In the second test case, a valid interval with maximum size is $ [4, 5] $ (it's valid because $ n = 40 $ is a multiple of $ 4 $ and $ 5 $ ) and its size is $ 2 $ . In the third test case, a valid interval with maximum size is $ [9, 11] $ . In the fourth test case, a valid interval with maximum size is $ [8, 13] $ . In the seventh test case, a valid interval with maximum size is $ [327869, 327871] $ .