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

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

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

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