A883. Up Down Subsequence--Platinum

Farmer John's $N$ cows ($2 \leq N \leq 3\cdot 10^5$), conveniently numbered $1
\ldots N$ as usual, have ordered themselves according to a permutation
$p_1,p_2,\ldots,p_N$ of $1\ldots N$. You are also given a string of length
$N-1$ consisting of the letters U and D. Please find the maximum $K\le N-1$
such that there exists a subsequence $a_0,a_1,\ldots,a_{K}$ of $p$ such that
for all $1\le j\le K$, $a_{j - 1} < a_j$ if the $j$th letter in the string is
U, and $a_{j - 1} > a_j$ if the $j$th letter in the string is D.

The first line contains $N$.
The second line contains $p_1,p_2,\ldots,p_N$.
The last line contains the string.

Write out maximum possible value of $K$.

We can choose $[a_0,a_1,a_2,a_3,a_4]=[p_1,p_2,p_3,p_4,p_5]$; the entire
permutation is consistent with the string.