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

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

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

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