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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 6 7 5 4 4 2 9 5 5 7 2 7 7 0 0 0 2 9 8 6 5 9 6 9 8 4 7 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