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:  4 3 5 3 4 3 3 5 4 9 5 7 5 9 8 0 0 0 0 0 0 5 3 9 8 4 3
Output: 4 3 3 5 4 9 5 7 5 9 8 0 0 0 0 0 0 5 3 9 8 4 3 4 3 5 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 7 6 0 0 6 1 6 9 5 2 6 9 6 2 2 5 5 1 6 8 3 3 6 5 7
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