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

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

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

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