Export Category with it's id in magento

<?php

ini_set('memory_limit', '-1');
set_time_limit(0);
    require_once('app/Mage.php');
    umask(0);
    Mage::app('default');
    define('MAGENTO', realpath(dirname(__FILE__)));
   
$file_path =  MAGENTO . '/var/export/catwithid.csv';
$mage_csv = new Varien_File_Csv();

$products_row = array();
$products_row['0']['categoryid'] = 'categoryid';
$products_row['0']['categoryname'] = 'categoryname';




$category = Mage::getModel ( 'catalog/category' );
    $tree = $category->getTreeModel ();
    $tree->load ();
   
    $ids = $tree->getCollection ()->getAllIds ();

foreach ($ids as $id)
{

    $data['categoryid'] = $id;
   
    $data['categoryname'] =  $category->load($id)->getName();

  $products_row[] = $data;
   
}
 




    $mage_csv->saveData($file_path, $products_row);
    echo "Please find test1.csv file in your folder.....";
   
   
    ?>