Output Format

For the plans of the $10$ states, output them in order.

For each state, first output a separate line indicating the state index, as shown in the sample.

Then output several lines, each containing $1$ integer, representing the number of bulbs per color in a valid partition.

Output in ascending order.

6
1,2,3,4,5

Case #1:
1
2
3
6
Case #2:
1
2
6
Case #3:
1
3
6
Case #4:
1
3
6
Case #5:
1
3
6
Case #6:
1
2
6
Case #7:
1
2
3
6
Case #8:
1
6
Case #9:
1
2
6
Case #10:
1
3
6

Hint

For $20\%$ of the testdata, $n \leq 3 \times 10^3$.

For $40\%$ of the testdata, $n \leq 5 \times 10^4$.

For $50\%$ of the testdata, $n \leq 10^5$.

For $60\%$ of the testdata, $n \leq 3 \times 10^5$.

For $70\%$ of the testdata, $n \leq 7 \times 10^5$.

For $100\%$ of the testdata, $1 \leq n \leq 1.2 \times 10^6$.

Translated by ChatGPT 5