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

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

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

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 0 6 2 2 4 6 9 1 9 6 3 2 8 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