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

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

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

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