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

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

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

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