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

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

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

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