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:  8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 6 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 6 2 8 0 0

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

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

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