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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 9 8 1 4 1 0 0 0 0 0 0 0 0 7 7 5 2 8 5 5 3 4
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