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

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

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