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

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

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

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