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

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

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

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 0 0 0 5 6 5 1 3 5 5 7 7 1 3 9 7 8
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