<|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 7 4 5 4 9 6 9 7 7 4 6 9 8 1 1 9 8 7 9
Output: 7 9 8 7 4 5 4 9 6 9 7 7 4 6 9 8 1 1 9 8

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 5 7 8 6 9 2 8 5 5 2 0 0 0 0 0 0 1 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user