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:  2 5 2 7 6 1 5 1 3 4 0 0 0 0 0 0 0 0 0 0 0 6 7 5 7 3 5 1 7
Output: 7 2 5 2 7 6 1 5 1 3 4 0 0 0 0 0 0 0 0 0 0 0 6 7 5 7 3 5 1

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

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

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