CMO 1990 Problem 2

Let $x$ be a natural number. We call $\{x_0,x_1,\dots ,x_l\}$ a factor linkof $x$ if the sequence $\{x_0,x_1,\dots ,x_l\}$ satisfies the following conditions: (1) $x_0=1, x_l=x$ ; (2) $x_{i-1}<x_i, x_{i-1}|x_i, i=1,2,\dots,l$ . Meanwhile, we define $l$ as the length of the factor link $\{x_0,x_1,\dots ,x_l\}$ . Denote by $L(x)$ and $R(x)$ the length and the number of the longest factor link of $x$ respectively. For $x=5^k\times 31^m\times 1990^n$ , where $k,m,n$ are natural numbers, find the value of $L(x)$ and $R(x)$ .