How to properly initialize a boost multi_array of objects?

I have been surprised to find that boost::multi_array seems to allocate its initial elements differently from, say, std::vector. It does not seem to fill each element with a unique element (using its default value or default constructor). I'm having trouble finding more information about this.

Is there a way to make the multi_array fill itself with a unique object at each element?

For example, consider the following:

static int num = 0;

struct A {
   int n;
   A() : n((::num)++) {
      std::cout << "A()" << std::endl;
   }
   virtual ~A() {}

   void print() {
      std::cout << "n=" << n << std::endl;
   }
};

int main() {
   std::cout << "vector:" << std::endl;
   std::vector<A> v(3);
   for (auto x : v) {
      x.print();
   }

   std::cout << "multi:" << std::endl;
   boost::multi_array<A, 2> m(boost::extents[2][2]);
   for (auto x : m) {
      for (auto y : x) {
         y.print();
      }
   }
}

This results in the output:

vector:
A()
A()
A()
n=0
n=1
n=2
multi:
A()
n=3
n=3
n=3
n=3

Why is the constructor called only once for the multi_array? How can the multi_array be "filled out" with unique objects (using A's default constructor)?