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次のプログラムは、Windows 7 の Chrome、Firefox、Safari で実行できますが、IE では実行できません。それを改善して簡潔に保つ方法は？

<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
    <title>选择地区</title>
  </head>
  <body>
    <form id="area">
      <select id="selectProvince" onchange="setCities()"></select>
      <select id="selectCity"></select>
    </form>
  </body>
  <script>
    var province_cities_map = {
        北京: ['东城','西城'],
        上海: ['黄浦','卢湾'],
    };
    function setProvinces() {
      provinces = Object.keys(province_cities_map);
      selectProvince.length = 0;
      for (i = 0; i < provinces.length; i++) selectProvince.options[i] = new Option(provinces[i]);
      setCities();
    }
    function setCities() {
      cities = province_cities_map[selectProvince.value];
      selectCity.length = 0;
      for (j = 0; j < cities.length; j++) selectCity.options[j] = new Option(cities[j]);
    }
    setProvinces();
  </script>
</html>
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