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Every member of Byteland Credit Society is entitled to loan any amount of Bytelandish ducats unless it is 1030 or more, but he has to return the whole amount within seven days. There are 100 ATMs in the Client Service Room of the Society. They are numbered from 0 to 99. Every ATM can perform one action only: it can pay or receive a fixed amount. The i-th ATM pays 2i ducats if i is even or it receives 2i ducats if i 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.
A client who is going to loan 7 ducats gets 16 ducats from the ATM No 4 and 1 ducat from the ATM No 0 and then he returns 8 ducats in the ATM No 3 and 2 ducats in the ATM No 1. In order to return the amount of 7 ducats he receives 1 ducat from the ATM No 0 and then he returns 8 ducats in ATM No 3.
Write a program that:
In the first line of the standard input there is one positive integer n ≤ 1,000, which equals the number of clients. In each of the following n lines there is one positive integer less than 1030 (at most 30 decimal digits). The number in the i-th line describes the amount which the client i is going to loan.
In each of 2n lines of the standard output there should be written a decreasing sequence of positive integers from the range [0..99] separated by single spaces, or one word NIE (which means “no” in Polish):
2 7 633825300114114700748351602698
4 3 1 0 3 0 NIE 99 3 1