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

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

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

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