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 $[327869, 327871]$ .