Programmatically set all form fields to ng-touched on form submission

if ($scope.form.$invalid) {
    angular.forEach($scope.form.$error, function (field) {
        angular.forEach(field, function(errorField){
            errorField.$setTouched();
        })
    });
    alert("Form is invalid.");
}

plunker:
http://plnkr.co/edit/XmvoTkIQ0yvFukrVSz11