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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 0 0 0 0 0 0 0 0 0 0 0 0 0 7 4 1 1 9 8 2 3
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