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

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

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

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