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

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

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

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