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

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

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

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