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

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

Example 3:
Input:  4 8 9 9 4 3 5 5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
Output: 8 9 9 4 3 5 5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4

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