D

Sum of Four Squares

You will be given an integer n, and you will have to express as summation of four square-numbers.

For example 30 can be written as summation of four squares in the following way:

30 = 4*4 +3*3 +2*2 + 1*1

If a number can be expressed as summation of four squares in more than one ways, any one of them will do. A square is a number whose square root is also an integer.

Input

Input starts with an integer T (≤ 120000), denoting the number of test cases.

Each case contains an integer n (0 ≤ n < 1017) in a line.

Output

For each case, print a line containing four integer numbers a, b, c, d such that

n = a2 + b2 + c2 + d2

If the number cannot be expressed as summation of four squares then you should print "Impossible." instead.

Sample Input

Output for Sample Input

 
3
30
2
0
 
5 2 0 1
1 0 0 1
0 0 0 0

Note

As the size of the input file is large, so use faster I/O functions like scanf(), printf().

Problem Setter: Shahriar Manzoor, Special Thanks: Jane Alam Jan