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

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

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

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