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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 7 7 7 4 3 9 3 5 8 8 3 1 5 8 9 6 2 7 0 0 0 1 2 6 4 7
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