First Round

By replacing each * in the expression $1\ast 2\ast 3\ast 4\ast 5\ast \cdots \ast 2019\ast 2020$ by a $+$ or a $-$ sign, we get a long calculation. Put the $+$ and $-$ signs in such a way that the outcome is a positive number (greater than $0$) which is as small as possible. What is this outcome?