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

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

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

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