recursively loop through nested JSON

HTML

<div id="list"></div>

JavaScript

var allData = {
    "Home": {
        "Home_Sub": ["home1", "home2", "home3"]
    },
        "About": ["about1", "about2", "about3"],
        "Contact": ["contact1", "contact2", "contact3"]
};

function printList(items) {
    switch ($.type(items)) {
        case "object":
            getChildren(items);
            break;
        case "string":
            console.log(items);
            break;
        case "array":
            printArray(items);
            break;
       
    }
}

function getChildren(parent) {
    for (var child in parent) {
        console.log(child);
        printList(parent[child]);
    }
}
function printArray(myArray){
    for(var i = 0; i < myArray.length; i++){
        console.log(myArray[i]);
        }
}
printList(allData);