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

Example 2:
Input:  2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2

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

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