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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 9 9 0 0 0 0 3 3 4 2 5 7 4 6
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