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Default Propagate Array Formula Down Column

Hi,

My situation:

Sheet1

A B C D E

1 Qty 4 1 2 3
2
3 DNG2 5 5 5 5
4 DNG3 2 4 7 1
5 DNG4 6 7 9 4
6 DNG5 2 2 3 6
7 DNG6 8 5 6 6


Sheet2

Total

DNG2 50


The Array Formula for calculating the Total for DNG2 is
{=SUMPRODUCT(Sheet1!$B$1:$E$1,Sheet1!B3:E3)}

How do I create a formula to calculate the Total Quantities for DNG3
through DNG6? This is in actually a much bigger list so I
want to be able to copy the formula down the column on Sheet2 and
auto-reference the proper rows in Sheet1.

Note: the Item Numbers (DNG2, DNG3, etc.) are unique.

Thanks,
Jim