Tomas received nine cards with the following numbers and mathematical symbols:

$$
18,19,20,20,+,-, \times,(,)
$$

He arranged the cards so that no two number cards were next to each other, meaning the number cards and symbol cards alternated. He then solved the resulting expressions and recorded the results.

Determine the largest result Tomas could have obtained.

(K. Pazourek)

Hint. Where could Tomas place the parentheses?
Tomáš had 4 cards with numbers and 5 cards with symbols. In the tasks he assembled, these two types of cards alternated, so each task started and ended with a symbol:

$$
\mathrm{S} \check{C} \mathrm{~S} \check{C} \mathrm{~S} \breve{C} \mathrm{~S} \check{C} \mathrm{~S}
$$

Before the left parenthesis and after the right parenthesis, there should be a symbol with some mathematical operation. To simultaneously meet the previous condition and ensure that the cards formed meaningful tasks, Tomáš had to place the parentheses at the edges as follows:

$$
\text { ( } \breve{C} S \breve{C} S \check{C} S \check{C} \text { ) }
$$

Multiplication and addition increase the result, with multiplication having a greater impact, while subtraction decreases the result. The largest possible result Tomáš could achieve was by multiplying the largest possible numbers, subtracting the smallest possible number, and adding the remaining number, for example:

$$
(20 \times 20-18+19),
$$

which equals 401.

Note. In the given solution, we did not consider the abbreviated notation for multiplying a number by a parenthesis. If we did, the largest result could be achieved as follows:

$$
+19(20 \times 20-18)
$$

which equals 7,258. Such a solution should also be evaluated as correct.