Using inputText inside ui:repeat to update ArrayList of values is not working [duplicate]

As referring to Post's title., I'm trying to update the values of ArrayList from h:inputText inside ui:repeat, which is not working.
Please see the following mock up for further understanding:

I have a POJO class as follows:

public class User implements Serializable{
    private String name;
    private List<String> emails;

    public User(String name, List<String> emails) {
        super();
        this.name = name;
        this.emails = emails;
    }
    //Setters Getters
}

In my Manager I have created list of User POJOS:

@ManagedBean
@ViewScoped
public class UserManager implements Serializable {
    private List<User> userList;
    public UserManager() {
        userList = new ArrayList<User>();
        ArrayList<String> emails= new ArrayList<String>();

        emails.add("[email protected]");
        emails.add("[email protected]");
        userList.add(new User("User1", (List<String>) emails.clone()));

        emails.clear();
        emails.add("[email protected]");
        emails.add("[email protected]");
        userList.add(new User("User2", (List<String>) emails.clone()));
    }
    public void action(){
    for(User u : userList){
        System.out.println(u);
    }
}
    //Setters Getters
}

Now in my Facelet I'm Using ui:repeat to load the data to h:inputText in to table, so that user can edit and change the values. Facelet Code:

<h:form id="userForm">
    <table border="1">
        <ui:repeat var="user" value="#{userManager.userList}">
            <tr>
                <td><h:inputText value="#{user.name}"/> </td>

                <ui:repeat var="email" value="#{user.emails}">
                    <td><h:inputText value="#{email}"/> </td>
                </ui:repeat>
            </tr>
        </ui:repeat>
    </table>

    <h:commandButton value="Save" action="#{userManager.action}">
        <f:ajax execute="@form @this"/>
    </h:commandButton>
</h:form>

The above approach works fine when I edit the #{user.name} but its not working with #{email}.
I can assume the its working for #{user.name} because name has setter and getter methods.
So how do I update the emails list object.
Is my POJO design is poor? or Is it a bad idea to use ui:repeat?
How can I achieve this?

Note: my current Mojarra version is 2.1