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:  2 0 0 0 0 0 0 0 0 0 0 0 0 8 9 1 7 8 1 1 4 8 4 6 9 8
Output: 0 0 0 0 0 0 0 0 0 0 8 9 1 7 8 1 1 4 8 4 6 9 8 2 0 0

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

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

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