Question 1
Function $F$, when applied to any four-digit positive integer $\overline{abcd}$, produces another positive integer, according to the rule: $F(\overline{abcd})=a^4+b^3+c^2+d^1$. For example, $F(2019)=2^4+0^3+1^2+9^1=26$.
Find the value of $F(2019)-F(2018)+F(2017)-F(2016)+\cdots-F(2000)$.
Find the value of $F(2019)-F(2018)+F(2017)-F(2016)+\cdots-F(2000)$.