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

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

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

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