MathDB

In a blackboard, it's written the following expression

1-2-2^2-2^3-2^4-2^5-2^6-2^7-2^8-2^9-2^{10}

We put parenthesis by different ways and then we calculate the result. For example:

1-2-\left(2^2-2^3\right)-2^4-\left(2^5-2^6-2^7\right)-2^8-\left( 2^9-2^{10}\right)= 403

and

1-\left(2-2^2 \left(-2^3-2^4 \right)-\left(2^5-2^6-2^7\right)\right)- \left(2^8- 2^9 \right)-2^{10}= -933

How many different results can we obtain?

Problem Statement