Perfect squares are fairly simple concept. A number like 49 is perfect square because it can be written as product of two same natural number i.e. 7 * 7.

On the other hand infinite sequence of numbers can be considered an intriguing concept, because it is not possible to represent all numbers belonging in an infinite sequence easily.

Can read more about infinite sequences here.

So one way to represent infinite sequence of numbers is to use an algebraic expression instead of writing all numbers in the sequence.

For example, expression x² + 1 represents the series 2, 5, 10, 17 .... . (Substituting value of x = 1, 2, 3, ... to get the values in the sequence)

Similarly x² + 4 represents the infinite series 5, 8, 13, 20, .... (Substituting value of x = 1, 2, 3, ... to get the values in the sequence)

Given an infinite sequence of numbers of form x² + n, figuring out perfect square numbers within this sequence can be challenging even if checking a number is perfect square is easy.

For example, consider the infinite sequence represented by x² + 771401, only when x = 385700 then x² + 771401 = 148765261401 = 385701² is a perfect square. There are no other values of x for which x² + 771401 will be a square.

This is because 771401 is difference between two consecutive squares 385700² and 385701². So the infinite sequence represented by x² + 771401 has only 1 perfect square number when x = 385701.

Let us consider one more example x² + 45, only when x = 2, 6 or 22 then x² + 45 is a perfect square. So the infinite sequence represented by x² + 45 has only 3 perfect square numbers when x = 2, 6 or 22.

But infinite sequence represented by x² + 46 contains no perfect square numbers, this is because if it contains such a number then the infinite sequence represented x² + 45 will not have any perfect square numbers which is a contradiction because we know 3 perfect square numbers contained in infinite sequence represented by x² + 45.

In other words given equation x² + n where n is a whole number (i.e. n can take values like 0, 1, 2, 3, 4 ...) find all x in ascending order such that x² + n is a perfect square.

Input

The first line of input file contains a positive integer 't' and next 't' lines contains a string which looks like 'x^2 + n' (example 'x^2 + 3', 'x^2 + 5' etc.).

0 ≤ n ≤ 10⁶ 

Sum of all 'n' in a test file will not exceed 10⁶

Output

The output line has to printed for each test case line.

If there are finite number of values of 'x' for which x² + n is a perfect square then print all such x in ascending order separated by comma and space (, ) and enclosed within square brackets. So for 'x^2 + 45' the output line will look like [2, 6, 22].

In case there are no such values of 'x' for which x² + n is a perfect square then print "No Solution" (without quotes and case sensitive). So for 'x^2 + 46' the output line will be "No Solution".

In case there are infinitely many solutions for which x² + n is a perfect square then print "Infinitely Many Solutions" (without quotes and case sensitive). So for 'x^2 + 0' the output line will be "Infinitely Many Solutions"

Example

Input:
3
x^2 + 45
x^2 + 0
x^2 + 46

Output:
[2, 6, 22]
Infinitely Many Solutions
No Solution