Divisors of the number#3702
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Divisors of the number

1 second
128 megabytes
Medium

Let's define the complexity of the number as the number of its divisors. Find among the numbers from to the most complex number. If there are several such numbers, find the smallest of them.

Input

First line contains the number of test cases (1 \le t \le 100). Each of the next lines contains one integer (1 \le n \le 10^{18}).

Output

For each test case print in a separate line the most complex number from to and its complexity.

Examples

Example 1

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