<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

Example 3:
Input:  6 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 7 4 7
Output: 7 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 7 4 7 6 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 3 4 5 8 6 2 1 2 4 6 1 3 6 2 1 0 9 8 6 9
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user