How to make range slider state update instantly?

Question

JavaScript

Essentially you need no additional plugins. The code I provide is working. What is missing is that the value in the field is updated as the slider is dragged, and not after it is released. How?

//Диапазон значений:
$(function(){
  $("input[type=range]").each(function(){
    $(this).wrap('<div class="range-wrapper"></div>');
    var min = $(this).attr("min");
    var max = $(this).attr("max");
    var step = $(this).attr("step");

    var input = $('<input class="narrow-input" type="number" min="'+min+
      '" max="'+max+
      '" step="'+step+'">');
    $(this).after(input);
    $(input).val($(this).val())
    $(this).change(function(){
      $(input).val($(this).val());
    })

    $(input).change(function(){
      $(input).prev().val($(input).val());
    })
  });
});
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