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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 1 5 2 2 6 8 7 0 0 0 0 0 0 0 0 0 3 4 8 6 7 7 6 1 6
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