Binomial coefficients

Binomial coefficients

Time limit 1 second
Memory limit 128 MiB

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 Ck_n is a number

where n and k are non-negative integers.

Gunnar used his program to calculate Ck_n 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 and k from the output he got. Can you help him and find all possible candidates?

Input data

First line contains the number of test cases, at most 100. Each test case is one line with an integer m (2m10^15) - the output of Gunnar's program.

Output data

For each test case print two lines. The first line must contain the number of ways of expressing m as a binomial coefficient. Print in the second one line all pairs (n, k) that satisfy Ck_n = 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.


Input example #1
Output example #1
(6,2) (6,4) (15,1) (15,14)
Source 2011 ACM Northwestern Europe (NWERC), Problem A