<|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:  2 7 8 4 7 3 4 6 6 2 8 0 0 0 0 0 8
Output: 4 7 3 4 6 6 2 8 0 0 0 0 0 8 2 7 8

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

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

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