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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
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