Novice's Mistake
Description
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.
Input
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.
Output
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.
3
2
3
10
3
20 18
219 216
2218 2214
1
165 162
1
1262 2519
Note
In the first example, $a = 20$, $b = 18$ are suitable, as "$\text{2}$" $\cdot 20 - 18 =$ "$\text{22222222222222222222}$"$- 18 = 22 = 2 \cdot 20 - 18$