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 () n = n! , k k!(n − k)! where n and k are non-negative integers. ( ) Gunnar used his program to calculate nk 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 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 ≤ 1015): the output of Gunnar’s program. Output 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 nk = 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)