linux - How do I swap Alt and Windows keys with xmodmap?

I have a Mac keyboard where the Alt/Win (i.e. Option/Command) keys are inverted compared to a regular PC keyboard, and I'd like to swap them. I haven't had any luck with xmodmap so far. The standard configuration is as follows:

shift       Shift_L (0x32),  Shift_R (0x3e)
lock        Caps_Lock (0x42)
control     Control_L (0x25),  Control_R (0x69)
mod1        Alt_L (0x40),  Alt_R (0x6c),  Meta_L (0xcd)
mod2        Num_Lock (0x4d)
mod3
mod4        Super_L (0x85),  Super_R (0x86),  Super_L (0xce),  Hyper_L (0xcf)
mod5        ISO_Level3_Shift (0x5c),  Mode_switch (0xcb)

Currently, the left/right alt keys are keycodes 64 and 108, while the left/right windows keys are 133 and 134.

I appreciate any help!