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

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

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

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