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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 4 7 3 9 3 4 8 1 9 4 0 0
Output: 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 4 7 3 9 3 4 8 1 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 3 7 7 1 4 6 5 1 0 8 1 9 6 3 7 2 2 5 4 9 3 8 7 8 7 2 8 3 6
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