You are a database expert and SQL optimizer. You will be given a SQL query and its rewritten variant. The rewritten query improves performance upon the original while maintaining equivalence. Your task is to create a new pair of original and rewritten queries that invoke a similar rewrite.

[ORIGINAL QUERY]```with ss_items as (select i_item_id item_id ,sum(ss_ext_sales_price) ss_item_rev from store_sales ,item ,date_dim where ss_item_sk = i_item_sk and d_date in (select d_date from date_dim where d_week_seq = (select d_week_seq from date_dim where d_date = '2001-06-16')) and ss_sold_date_sk = d_date_sk group by i_item_id), cs_items as (select i_item_id item_id ,sum(cs_ext_sales_price) cs_item_rev from catalog_sales ,item ,date_dim where cs_item_sk = i_item_sk and d_date in (select d_date from date_dim where d_week_seq = (select d_week_seq from date_dim where d_date = '2001-06-16')) and cs_sold_date_sk = d_date_sk group by i_item_id), ws_items as (select i_item_id item_id ,sum(ws_ext_sales_price) ws_item_rev from web_sales ,item ,date_dim where ws_item_sk = i_item_sk and d_date in (select d_date from date_dim where d_week_seq =(select d_week_seq from date_dim where d_date = '2001-06-16')) and ws_sold_date_sk = d_date_sk group by i_item_id) select ss_items.item_id ,ss_item_rev ,ss_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 ss_dev ,cs_item_rev ,cs_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 cs_dev ,ws_item_rev ,ws_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 ws_dev ,(ss_item_rev+cs_item_rev+ws_item_rev)/3 average from ss_items,cs_items,ws_items where ss_items.item_id=cs_items.item_id and ss_items.item_id=ws_items.item_id and ss_item_rev between 0.9 * cs_item_rev and 1.1 * cs_item_rev and ss_item_rev between 0.9 * ws_item_rev and 1.1 * ws_item_rev and cs_item_rev between 0.9 * ss_item_rev and 1.1 * ss_item_rev and cs_item_rev between 0.9 * ws_item_rev and 1.1 * ws_item_rev and ws_item_rev between 0.9 * ss_item_rev and 1.1 * ss_item_rev and ws_item_rev between 0.9 * cs_item_rev and 1.1 * cs_item_rev order by item_id ,ss_item_rev limit 100;```

[REWRITTEN QUERY]```with dates as (select d_date from date_dim where d_week_seq = (select d_week_seq from date_dim where d_date = '2001-06-16')), ss_items as (select i_item_id item_id ,sum(ss_ext_sales_price) ss_item_rev from store_sales ,item ,date_dim where ss_item_sk = i_item_sk and d_date in (select d_date from dates) and ss_sold_date_sk = d_date_sk group by i_item_id), cs_items as (select i_item_id item_id ,sum(cs_ext_sales_price) cs_item_rev from catalog_sales ,item ,date_dim where cs_item_sk = i_item_sk and d_date in (select d_date from dates) and cs_sold_date_sk = d_date_sk group by i_item_id), ws_items as (select i_item_id item_id ,sum(ws_ext_sales_price) ws_item_rev from web_sales ,item ,date_dim where ws_item_sk = i_item_sk and d_date in (select d_date from dates) and ws_sold_date_sk = d_date_sk group by i_item_id) select ss_items.item_id ,ss_item_rev ,ss_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 ss_dev ,cs_item_rev ,cs_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 cs_dev ,ws_item_rev ,ws_item_rev/((ss_item_rev+cs_item_rev+ws_item_rev)/3) * 100 ws_dev ,(ss_item_rev+cs_item_rev+ws_item_rev)/3 average from ss_items,cs_items,ws_items where ss_items.item_id=cs_items.item_id and ss_items.item_id=ws_items.item_id and ss_item_rev between 0.9 * cs_item_rev and 1.1 * cs_item_rev and ss_item_rev between 0.9 * ws_item_rev and 1.1 * ws_item_rev and cs_item_rev between 0.9 * ss_item_rev and 1.1 * ss_item_rev and cs_item_rev between 0.9 * ws_item_rev and 1.1 * ws_item_rev and ws_item_rev between 0.9 * ss_item_rev and 1.1 * ss_item_rev and ws_item_rev between 0.9 * cs_item_rev and 1.1 * cs_item_rev order by item_id ,ss_item_rev limit 100;```

Now, consider the TPC-DS schema and create a new original and equivalent rewritten query pair such that the rewrite operation is similar to the provided demonstration.Keep the following points in mind while creating the new query pair:
1. The original query must contain CTEs.
2. The original query must make use of the following fact tables: ['inventory']. Below is the join graph for these fact tables:
    ['inventory(inv_warehouse_sk) references warehouse(w_warehouse_sk);', 'inventory(inv_date_sk) references date_dim(d_date_sk);', 'inventory(inv_item_sk) references item(i_item_sk);']
4. The original query must employ 0 joins.
5. The original query must employ the following operators in its WHERE clause: ['avg', 'sum', 'max'].
6. The rewritten query must be equivalent to the original query, and must follow a similar rewrite pattern as in the given example. Enclose the original and rewritten queries within ``` and ```.