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

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

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

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