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

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

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

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