dp
of length numPeople / 2 + 1
and set dp[0] = 1
.i
from 1
to numPeople / 2
inclusive.
i
, iterate j
from 0
to i - 1
inclusive.dp[i]
by adding dp[j] * dp[i - j - 1]
to it, modulo 10^9 + 7
.dp[numPeople / 2]
as the final answer.