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

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

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