  We study the problem of storing the minimum number of bits required to answer
next/previous larger/smaller value queries on an array $A$ of $n$ numbers,
without storing $A$. We show that these queries can be answered by storing at
most $3.701 n$ bits. Our result improves the result of Jo and Satti [TCS 2016]
that gives an upper bound of $4.088n$ bits for this problem.
