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

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

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

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