[Plugin: Woocommerce] Add free product if cart has 3 items

What I’m trying to do is to add free product if user have 3 product in cart. I choosed woocommerce_add_cart_item hook for this. Here is my code :

add_filter('woocommerce_add_cart_item', 'set_item_as_free', 99, 1);

function set_item_as_free($cart_item) {

    global $woocommerce;
    $products_with_price = 0;

    foreach ( $woocommerce->cart->get_cart() as $cart_item_key => $values ) {
        if($values['data']->price == 0) {
            continue;
        } else {
            $products_with_price++;
        }
    }

    if( $products_with_price > 1 && $products_with_price % 3 == 1) {
        $cart_item['data']->set_price(0);
        return $cart_item;
    }
    return $cart_item;

}

I also tried $cart_item['data']->price = 0; but it doesn’t work out either ?? Is there is something I do wrong or maybe there is some other way to get this done? Thanks.