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

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

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

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