Three numbers are chosen at random, one after another with replacement, from the set \( S=\{1,2,3,\ldots,100\} \). Let \( p_1 \) be the probability that the maximum of chosen numbers is at least \( 81 \) and \( p_2 \) be the probability that the minimum of chosen numbers is at most \( 40 \).
The value of \( \frac{625}{4}\, p_1 \) is ______.
