Problem #281
Open Sets
Let n = 192837. For each i from 1 to n, let x_i and y_i be two independently chosen random numbers from (0, 1). Let a_i = \min (x_i, y_i), b_i = \max (x_i, y_i), and S be the intersection of open intervals (a_i, b_i). In other words,
S = \bigcap_{i = 1}^n (a_i, b_i)
It is easy to see that S is itself an open interval. Find the expected length of S.
It can be shown that the answer can be expressed as \frac{p}{q}, where \gcd(p,q) = 1 and q \neq 0 \mod 998244353. Output pq^{-1} \mod 998244353.