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:  3 8 8 9 2 4 0 0 0 0 0 0 0 0 0 0 0 0 7 3 2 9 8 5 1 9 3 9 7
Output: 8 8 9 2 4 0 0 0 0 0 0 0 0 0 0 0 0 7 3 2 9 8 5 1 9 3 9 7 3

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

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

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