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

Example 2:
Input:  0 9 7 5 2 7 7 7 3 0 0 0 0 0 0 0 0 0 0 0
Output: 7 5 2 7 7 7 3 0 0 0 0 0 0 0 0 0 0 0 0 9

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

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