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 9 2 3 8 8 4 7 9 4 9 7 7 9 3 2
Output: 8 8 4 7 9 4 9 7 7 9 3 2 7 9 2 3

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 3 3 0 0 4 5 1 1 8 7 6 5 1 3 2
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