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

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

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

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