ATMs

Memory limit: 32 MB

Every member of Byteland Credit Society is entitled to loan any amount of Bytelandish ducats unless it is or more, but he has to return the whole amount within seven days. There are ATMs in the Client Service Room of the Society. They are numbered from to . Every ATM can perform one action only: it can pay or receive a fixed amount. The -th ATM pays ducats if is even or it receives ducats if is odd. If a client is going to loan a fixed sum of money it is necessary to check if he is able to get the money using every ATM at most once. If so, numbers of ATMs he has to use should be determined. It is also necessary to check if the client can return the money in a similar way, and if so, to determine numbers of ATMs he has to use.

Example

A client who is going to loan ducats gets ducats from the ATM No and ducat from the ATM No and then he returns ducats in the ATM No and ducats in the ATM No . In order to return the amount of ducats he receives ducat from the ATM No and then he returns ducats in ATM No .

Task

Write a program that:

• reads the number of clients from the standart input and then, for every client reads from the same file the amount of money he is going to loan;
• checks for every client if he is able to get the money using every ATM at most once and if so, determines the numbers of ATMs he has to use;
• writes the results to the standard output.

Input

In the first line of the standard input there is one positive integer , which equals the number of clients. In each of the following lines there is one positive integer less than (at most decimal digits). The number in the -th line describes the amount which the client is going to loan.

Output

In each of lines of the standard output there should be written a decreasing sequence of positive integers from the range separated by single spaces, or one word NIE (which means “no” in Polish):

• in the first line of the -th pair of lines there should be numbers of ATMs (in decreasing order) that the client should use to get his loan or one word NIE if the loan cannot be received according to the rules;
• in the second line of the -th pair there should be numbers of ATMs (in decreasing order) which the client should use to return his loan or the word NIE.

Example

For the input data:

2
7
633825300114114700748351602698

the correct result is:

4 3 1 0 
3 0 
NIE
99 3 1 

Task author: Piotr Chrzastowski-Wachtel.