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

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

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

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