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

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

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

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