Enter a integer then check whether it is positive or negative.

Input

The first line of the input consist of a single integer number t which determines the number of tests.

In each of next t lines there is a single integer n.

Constraints

• 0 < t ≤ 1 000
• - 1 000 000 ≤ n ≤ 1 000 000

Output

For each number n print out the result in format " is positive integer" or " is negative integer" or "n is zero".

Separate your answers with a new line character.

Example

Input:
5
-7
9
0
4
-3

Output:
-7 is negative number 
9 is positive number 
n is zero 
4 is positive number 
-3 is negative number