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:  4 3 3 9 4 3 1 1 4 0 0 0 0 0 0 0 0 0 1 3 8 3 5
Output: 3 8 3 5 4 3 3 9 4 3 1 1 4 0 0 0 0 0 0 0 0 0 1

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

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

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