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 4 2 9 4 7 4 3 1 6 1 3 6 0 0 0 0 0 0 0 0 0 0 0 0
Output: 4 2 9 4 7 4 3 1 6 1 3 6 0 0 0 0 0 0 0 0 0 0 0 0 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 3 8 5 5 6 7 1 3 2 1 2 9 9 1 5 1 8 0 1 5 8 3 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