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

Example 2:
Input:  9 7 4 2 4 5 0 0 0 0 0 0 0 0 0 0 9
Output: 7 4 2 4 5 0 0 0 0 0 0 0 0 0 0 9 9

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

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