E. Novice's Mistake
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$n \cdot a - b$$$.

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.

Example
Input
3
2
3
10
Output
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 "$$$\text{2}$$$" $$$\cdot 20 - 18 =$$$ "$$$\text{22222222222222222222}$$$"$$$- 18 = 22 = 2 \cdot 20 - 18$$$