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

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

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

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