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

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

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

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