I'm trying to reduce the number of colors in the image below using -remap in imagemagick.

olympic-logo.png
[![olympic-logo.png](https://i.stack.imgur.com/LFpzT.png)](https://i.stack.imgur.com/LFpzT.png)

colortable.png which consists of this two color A12E64, FF0000

[![enter image description here](https://i.stack.imgur.com/3yRxx.png)](https://i.stack.imgur.com/3yRxx.png)

Using the following code:

```
convert olympic-logo.png +dither -remap colortable.png olympic-logo-remap.png

```

Output: 
olympic-logo-remap.png

[![enter image description here](https://i.stack.imgur.com/lyqpr.gif)](https://i.stack.imgur.com/lyqpr.gif)

Expected Output:
olympic-logo-expected.png
[![enter image description here](https://i.stack.imgur.com/mWBjM.png)](https://i.stack.imgur.com/mWBjM.png)

Is there a way to ignore transparent area so It won't get mapped to get the expected output?

Thanks and more power.