Description

Given a positive integer n and the odd integer o and the nonnegative integer p such that n = o2^p. 


Example 

For n = 24, o = 3 and p = 3. 


Task 

Write a program which for each data set: 

reads a positive integer n, 

computes the odd integer o and the nonnegative integer p such that n = o2^p, 

writes the result. 

Input

The first line of the input contains exactly one positive integer d equal to the number of data sets, 1 <= d <= 10. The data sets follow. 

Each data set consists of exactly one line containing exactly one integer n, 1 <= n <= 10^6. 

Output

The output should consists of exactly d lines, one line for each data set. 

Line i, 1 <= i <= d, corresponds to the i-th input and should contain two integers o and p separated by a single space such that n = o2^p. 

Sample Input

1 
24 

Sample Output

3 3 

HINT

Source

Central Europe 2001, Practice