Gunnar is quite an old and forgetful researcher. Right now he is writing a paper on security in social networks and it actually involves some combinatorics. He wrote a program for calculating binomial coefficients to help him check some of his calculations. A binomial coefficient is a number where n and k are non-negative integers. Gunnar used his program to calculate and got a number m as a result. Unfortunately, since he is forgetful, he forgot the numbers n and k he used as input. These two numbers were a result of a long calculation and they are written on one of many papers lying on his desk. Instead of trying to search for the papers, he tried to reconstruct the numbers n, k from the output he got. Can you help him and find all possible candidates?

On the first line a positive integer: the number of test cases, at most 100. After that per test case:  one line with an integer m (2 <= m <= 10^15): the output of Gunnar’s program.

Per test case:  one line with an integer: the number of ways of expressing m as a binomial coefficient.  one line with all pairs (n; k) that satisfy = m. Order them in increasing order of n and, in case of a tie, order them in increasing order of k. Format them as in the sample output.

NWERC2011