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

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

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

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