  Denote by $u(n)$ the largest principal specialization of the Schubert
polynomial: $ u(n) := \max_{w \in S_n} \mathfrak{S}_w(1,\ldots,1) $ Stanley
conjectured in [arXiv:1704.00851] that there is a limit $\lim_{n\to \infty} \,
\frac{1}{n^2} \log u(n), $ and asked for a limiting description of permutations
achieving the maximum $u(n)$. Merzon and Smirnov conjectured in
[arXiv:1410.6857] that this maximum is achieved on layered permutations. We
resolve both Stanley's problems restricted to layered permutations.
