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

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

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

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 5 9 6 7 2 5 5 0 0 0 0 0 0 0 0 0 0 0 0
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