A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 2 0 0 0 0 1 0 3 5 1 3 0 0 0 0 0 2 0 0 3 7 4 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>.
Assistant: Let me solve this step by step.
<think>
user