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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 8 5 2 3 2 1 6 8 2 6 6 0 0 0 0 2 6 7 4 9 6 4 7 3 5 5
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