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

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

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

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