Every positive integer $$k$$ has a unique factorial base expansion $$(f_1,f_2,f_3,\ldots,f_m)$$, meaning that $$k=1!\cdot f_1+2!\cdot f_2+3!\cdot f_3+\cdots+m!\cdot f_m$$, where each $$f_i$$ is an integer, $$0\le f_i\le i$$, and $$0< f_m$$. Given that $$(f_1,f_2,f_3,\ldots,f_j)$$ is the factorial base expansion of $$16!-32!+48!-64!+\cdots+1968!-1984!+2000!$$, find the value of $$f_1-f_2+f_3-f_4+\cdots+(-1)^{j+1}f_j$$.

(第十八届AIME2 2000 第14题)