A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  9 3 7 6 9 9 4 0 0 0 9 8 1 6 8 3 7 4 7 7 2 1 5 4 6 6 6 1
Output: 6 6 1 9 3 7 6 9 9 4 0 0 0 9 8 1 6 8 3 7 4 7 7 2 1 5 4 6

Example 2:
Input:  4 9 8 5 8 3 7 8 5 9 1 9 6 1 2 9 7 5 4 1 3 5 8 7 7 2 5 7
Output: 2 5 7 4 9 8 5 8 3 7 8 5 9 1 9 6 1 2 9 7 5 4 1 3 5 8 7 7

Example 3:
Input:  9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6
Output: 0 3 6 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 3 4 1 1 2 1 3 2 3 3 1 1 8 9 6 1 9 2 9 4 6 5 6 5 2 0
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user