  In this paper we examine the problem of computing majority function
$\mathrm{MAJ}_n$ on $n$ bits by depth-two formula, where each gate is a
majority function on at most $k$ inputs. We present such formula that gives the
first nontrivial upper bound for this problem, with $k = \frac{2}{3} n + 4$.
This answers an open question in [Kulikov, Podolskii, 2017].
  We also look at this problem in adaptive setting - when we are allowed to
query for value of $\mathrm{MAJ}_k$ on any subset, and wish to minimize the
number of such queries. We give a simple lower bound for this setting with
$\lceil n/k \rceil$ queries, and we present two algorithms for this model: the
first one makes $\approx 2\frac{n}{k} \log k$ queries in the case when we are
limited to the standard majority functions, and the second one makes
$\frac{n}{k} \log k$ queries when we are allowed to change the threshold of
majority function.
