# Биномиальный коэффициент

# Binomial coefficients

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

First line contains the number of test cases, at most **100**. Each test case is one line with an integer **m** (**2** ≤ **m** ≤ `10`

) - the output of Gunnar's program.^{15}

#### Output

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.

2 2 15

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