firebase security permission not working

Question

I have below data stored in my firebase:

firebaseRoot
    admins
        simplelogin:1: 
    users
        simplelogin:1
            email: abc@xyz.com
            picture: csd
            provider: password
            uid: simplelogin:1
        simplelogin:2
            email: abc1@xyz.com
            picture: zsd
            provider: password
            uid: simplelogin:1

and following security rules:

{
  "rules": {
    "admins": {
      ".read": "root.child('admins').child(auth.uid).val() === true",
      ".write": "root.child('admins').child(auth.uid).val() === true"
    },
    "users": {
      "$user":{
        ".read": "$user === auth.id || root.child('admins').child(auth.uid).val() === true",
        ".write": "$user === auth.id"
      }
    }
  }
}

My authorization requirements are as below.

1. admins can be read and added only by the existing admin only. This works.
2. All users can be read by the admin but should not be able to write user data.
3. a user can read and update his own user data.

Currently with above rules, I am not able read users data both for admins and logged in users. I get below error message. Please provide your help. Thanks.

var rootRef = new Firebase('https://xxxxx.firebaseio.com/');
var users = rootRef.child('users');
users.on('value', function(snap) {
console.log(snap.key(), snap.val());
}, function(error) {
console.log(error);
});

Error:

Error: permission_denied: Client doesn't have permission to access the desired data.

Answer 1

Waitting for answers