| # Meituan Cup Warm-up Problem — Number Loop | |
| This year's Meituan Cup warm-up problem is a **Number Loop**. | |
| When designing this problem, Suanxie first selected the following template, ensuring that the puzzle must contain the two patterns **MT** and **PKU**. | |
| The next step is to replace all `?` in the template with digits from `0` to `3`, thus forming a valid Number Loop puzzle. An important requirement is that the puzzle must have a **unique solution** (the definition of a solution can be found in the warm-up problem). | |
| However, Suanxie found that creating a puzzle of suitable difficulty with a unique solution on this template was extremely challenging. Therefore, he temporarily modified the template, which resulted in the final warm-up problem used in the contest. | |
| Although he eventually managed to produce a valid puzzle, the feeling of failure still bothered him. Now, he hopes that you can help him achieve his original goal — **to construct a unique-solution Number Loop puzzle based on the original template.** | |
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| ## Problem Description | |
| You need to construct a valid Number Loop puzzle according to the given input type. | |
| * If the input is `0`, this corresponds to the **Small Task**: replace all `?` in the template with integers from `0` to `3`, ensuring the resulting puzzle has a **unique solution**. | |
| * If the input is `1`, this corresponds to the **Large Task**: replace all `?` in the template with integers from `1` to `3`, ensuring the resulting puzzle has a **unique solution**. | |
| Your program should output a $12\times12$ grid consisting only of spaces and digits `0`–`3`, representing the constructed puzzle. Each row of the grid corresponds to one line of output (including spaces). | |
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| ## Input Format | |
| The input contains a single integer: | |
| * `0` — requires output of the Small Task solution. | |
| * `1` — requires output of the Large Task solution. | |
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| ## Output Format | |
| Output a $12\times12$ character matrix containing only spaces and digits `0`–`3`, representing your constructed Number Loop puzzle. | |
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| ## Sample Output | |
| Below is a sample output (note that this example has **multiple solutions** and therefore does **not** satisfy the problem requirement; it is shown only to illustrate the format): | |
| ``` | |
| 0 0 000 | |
| 00 00 0 0 | |
| 0 0 0 0 0 | |
| 0 0 0 0000 | |
| 0 0 0 0 | |
| 0 0 0 | |
| 0 0 00000 | |
| 0 0 0 | |
| 00 0 0 0 | |
| 0 0 0 0 0 | |
| 0 0 000 0 | |
| ``` | |