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

Example 2:
Input:  6 6 8 1 1 6 6 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 7 6 7 7
Output: 8 1 1 6 6 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 7 6 7 7 6 6

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

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