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:  3 4 4 4 7 0 0 0 0 0 0 0 0 0 0 0 9 9 6
Output: 4 4 4 7 0 0 0 0 0 0 0 0 0 0 0 9 9 6 3

Example 2:
Input:  5 0 0 0 0 0 0 0 0 0 0 0 1 1 9 2 7 9 2
Output: 0 0 0 0 0 0 0 0 0 0 0 1 1 9 2 7 9 2 5

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 2 4 2 4 2 9 8 6 4 7 6 1 1 3 3 4 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