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

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

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

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