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 8 3 5 1 3 3 1 8 5 8 5 3 2 8 0 0 0 0 0 0 0 0 0 0 0 2 4
Output: 3 5 1 3 3 1 8 5 8 5 3 2 8 0 0 0 0 0 0 0 0 0 0 0 2 4 3 8

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 3 1 1 1 9 1 8 3 5 3 0 0 0 0 0 0 0 0 1 8 3 8 3 2 3 6 3
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