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

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

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

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