CF1992E Novice's Mistake

One of the first programming problems by K1o0n looked like this: "Noobish\_Monk has $ n $ $ (1 \le n \le 100) $ friends. Each of them gave him $ a $ $ (1 \le a \le 10000) $ apples for his birthday. Delighted with such a gift, Noobish\_Monk returned $ b $ $ (1 \le b \le \min(10000, a \cdot n)) $ apples to his friends. How many apples are left with Noobish\_Monk?" K1o0n wrote a solution, but accidentally considered the value of $ n $ as a string, so the value of $ n \cdot a - b $ was calculated differently. Specifically: - when multiplying the string $ n $ by the integer $ a $ , he will get the string $ s=\underbrace{n + n + \dots + n + n}_{a\ \text{times}} $ - when subtracting the integer $ b $ from the string $ s $ , the last $ b $ characters will be removed from it. If $ b $ is greater than or equal to the length of the string $ s $ , it will become empty. Learning about this, ErnKor became interested in how many pairs $ (a, b) $ exist for a given $ n $ , satisfying the constraints of the problem, on which K1o0n's solution gives the correct answer. "The solution gives the correct answer" means that it outputs a non-empty string, and this string, when converted to an integer, equals the correct answer, i.e., the value of $ n \cdot a - b $ .

The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. For each test case, a single line of input contains an integer $ n $ ( $ 1 \le n \le 100 $ ). It is guaranteed that in all test cases, $ n $ is distinct.

For each test case, output the answer in the following format: In the first line, output the integer $ x $ — the number of bad tests for the given $ n $ . In the next $ x $ lines, output two integers $ a_i $ and $ b_i $ — such integers that K1o0n's solution on the test " $ n $ $ a_i $ $ b_i $ " gives the correct answer.

In the first example, $ a = 20 $ , $ b = 18 $ are suitable, as " $ \text{2} $ " $ \cdot 20 - 18 = $ " $ \text{22222222222222222222} $ " $ - 18 = 22 = 2 \cdot 20 - 18 $