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

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

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