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 5 8 0 0 0 0 0 0 0 0 0 0 5 8 5 1 5 4 9 7 1
Output: 0 0 0 0 0 0 0 0 0 0 5 8 5 1 5 4 9 7 1 9 5 8

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

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

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