Royal Seafood delivers fresh fin and shellfish to specialty grocery stores in the state of Oregon. The company packs a delivery truck in Corvallis and then drives in one single route to its $5$ customers spread throughout the state. The distances in miles between all locations may be found in the Table $1.$

Corvallis$($A$)$

Roseburg$($B$)$

Bend$($C$)$

Baker$($D$)$

Lakeview$($E$)$

Burns$($F$)$

Corvallis$($A$)$

$$

$233$

$242$

$241$

$177$

$197$

Roseburg$($B$)$

$233$

$$

$167$

$252$

$273$

$176$

Bend$($C$)$

$242$

$167$

$$

$261$

$254$

$205$

Baker$($D$)$

$241$

$252$

$261$

$$

$161$

$295$

Lakeview$($E$)$

$177$

$273$

$254$

$161$

$$

$179$

$$Burns$($F$)$

$197$

$176$

$205$

$295$

$179$

$$

Part $2$

a$.$ Propose an efficient route by using the Nearest Neighbor heuristic with Corvallis as the starting city. What is the total distance$$ traveled?