The RSA encryption is based on the following procedure:

Generate two distinct primes $p$ and $q$.
Compute $n=pq$ and $\varphi =(p-1)(q-1)$.
Find an integer $e$, $1<e<\varphi$, such that $gcd(e,\varphi )=1$.

A message in this system is a number in the interval $[0,n-1]$.
A text to be encrypted is then somehow converted to messages (numbers in the interval $[0,n-1]$).
To encrypt the text, for each message, $m$, $c=m^{e}modn$ is calculated.

To decrypt the text, the following procedure is needed: calculate $d$ such that $ed=1mod\varphi$, then for each encrypted message, $c$, calculate $m=c^{d}modn$.

There exist values of $e$ and $m$ such that $m^{e}modn=m$.
We call messages $m$ for which $m^{e}modn=m$ unconcealed messages.

An issue when choosing $e$ is that there should not be too many unconcealed messages.
For instance, let $p=19$ and $q=37$.
Then $n=19\cdot 37=703$ and $\varphi =18\cdot 36=648$.
If we choose $e=181$, then, although $gcd(181,648)=1$ it turns out that all possible messages $m$ ($0\le m\le n-1$) are unconcealed when calculating $m^{e}modn$.
For any valid choice of $e$ there exist some unconcealed messages.
It's important that the number of unconcealed messages is at a minimum.

Choose $p=1009$ and $q=3643$.
Find the sum of all values of $e$, $1<e<\varphi (1009,3643)$ and $gcd(e,\varphi )=1$, so that the number of unconcealed messages for this value of $e$ is at a minimum.