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

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

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