Static variables in member functions

Can someone please explain how static variables in member functions work in C++.

Given the following class:

class A {
   void foo() {
      static int i;
      i++;
   }
}

If I declare multiple instances of A, does calling foo() on one instance increment the static variable i on all instances? Or only the one it was called on?

I assumed that each instance would have its own copy of i, but stepping through some code I have seems to indicate otherwise.