Angular 1.3 - Using ngMessages for digits only validation

Question

I'm using ngMessages in my form. I have one field I want the user to be able to insert digits only. If the user type some letters that are not numbers (e.g not 0-9) nothing will be shown in the field. In addition, I want to use ng-min and ng-max to validate the inserted value. So I created a directive but in order to use ng-min and ng-max I need to use "type=number" which ruins my directive behavior...

This is the field from my form:

  <div class="field">
      <label for="age">insert your age</label>
      <input name="age"
                   ng-model="data.age"
                   ng-minlength="1"
                   ng-maxlength="2"
                   ng-min="10"
                   ng-max="80"
                   only-digits 
                   type="number"
                   required/>

      <div class="error-messages" ng-messages="userForm.age.$error">
            <div ng-message="required">You left the field blank...</div>
            <div ng-message="minlength">Your field is too short</div>
            <div ng-message="maxlength">Your field is too long</div>
            <div ng-message="min">You must be at least 10 years old!</div>
            <div ng-message="max">You must be less than 80 years old!</div>    
      </div>

  </div>

And my directive is:

angular.module('directives').
directive('onlyDigits', function () {

    return {
        restrict: 'A',
        require: '?ngModel',
        scope: {
        },
        link: function (scope, element, attrs, ngModel) {
            if (!ngModel) return;
            ngModel.$parsers.unshift(function (inputValue) {
                var digits = inputValue.split('').filter(function (s) { return (!isNaN(s) && s != ' '); }).join('');
                ngModel.$setViewValue(digits, "");
                ngModel.$render();
                return digits;
            });
        }
    };
});