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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 0 0 0 0 1 5 5 3 9 4 3 7 6 7 8 5 7 9 7 3 1 7 7 6 2 4 6
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