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

$$\displaystyle \binom n k = \frac{n!}{k! (n-k)!},$$

where ~n~ and ~k~ are non-negative integers.

Gunnar used his program to calculate ~\binom n k~ 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?

Input Specification

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 \le m \le 10^{15})~: the output of Gunnar's program.

Output Specification

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 ~\binom n k = 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.

Sample Input

2
2
15

Sample Output

1
(2,1)
4
(6,2) (6,4) (15,1) (15,14)