Collect a flat array of objects as nested map

flat-to-tree.js

var flat = [
  { id: "A", name: "A", parent: "" },
  { id: "B", name: "B", parent: "" },
  { id: "C", name: "C", parent: "D" },
  { id: "D", name: "D", parent: "B" },
  { id: "E", name: "E", parent: "A" }
];

function unflatten(list) {
  return; //...
}

unflatten(flat); // should return:

var desiredOut = {
  A: {
    id: "A",
    name: "A",
    children: {
      E: {
        id: "E",
        name: "E",
        children: {}
      }
    }
  },
  B: {
    id: "B",
    name: "B",
    children: {
      D: {
        id: "D",
        name: "D",
        children: {
          C: {
            id: "C",
            name: "C",
            children: {}
          }
        }
      }
    }
  }
};