Description:
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).
Input Format:
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 $$$n$$$ ($$$1 \leq n \leq 10^{18}$$$).
Output Format:
For each test case, print a single integer: the maximum size of a valid interval.
Note:
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 $$$[327869, 327871]$$$.