A. Balanced Tripartition
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are given a positive integer $$$n \gt 1$$$. Your task is to partition the set $$$\{1, 2, ..., 3n\}$$$ into three sets $$$A$$$, $$$B$$$, and $$$C$$$, each containing $$$n$$$ elements. The sets $$$A$$$, $$$B$$$, and $$$C$$$ should have the same sum. It can be shown that under the given constraints, a valid partition always exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 50$$$). The description of the test cases follows.

Each test case consists of a single line containing an integer $$$n$$$ ($$$2 \le n \le 1000$$$) — the required size of each set.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$1000$$$.

Output

For each test case, output a single line consisting of $$$3n$$$ characters. Each character should be either A, B, or C (upper or lower case). The character at position $$$i$$$ indicates which set the number $$$i$$$ belongs to ($$$A$$$, $$$B$$$, or $$$C$$$).

If there are multiple solutions, you may print any.

Example
Input
2
4
5
Output
ABBCCCAABACB
ABABCCBCACCBAAB
Note

In the first test case, $$$n = 4$$$, so we are splitting up the numbers from $$$1$$$ to $$$3 \cdot 4 = 12$$$. One solution is to partition these numbers into $$$A = \{1, 7, 8, 10\}$$$, $$$B = \{2, 3, 9, 12\}$$$, and $$$C = \{4, 5, 6, 11\}$$$. Each of these sets contains $$$4$$$ numbers and sums to $$$26$$$. Since $$$1$$$ is in $$$A$$$, the first character of our output is A. Since $$$2$$$ is in $$$B$$$, the second character of our output is B. Carrying on this process, we obtain the output ABBCCCAABACB.