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 0 0 0 0 0 0 0 0 0 0 7 4 7 5 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 4 7 5 0 0 0 0 0 0 0 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 6 6 9 6 8 7 9 6 8 3 5 9 6 0 0 0 0 0 5 9 7 7 1 9 9 7 4 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