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

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

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

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