Why doesn't C# let you declare multiple variables using var?

Question

Given the following:

// not a problem
int i = 2, j = 3;

so it surprises me that this:

// compiler error: Implicitly-typed local variables cannot have multiple declarators
var i = 2, j = 3;

doesn't compile. Maybe there is something I don't understand about this (which is why I'm asking this)?

But why wouldn't the compiler realize that I meant:

var i = 2;
var j = 3;

which WOULD compile.