Some people know each other in a group of people, where "knowing" is a symmetric relation. For a person, we say that it is $social$ if it knows at least $20$ other persons and at least $2$ of those $20$ know each other. For a person, we say that it is $shy$ if it doesn't know at least $20$ other persons and at least $2$ of those $20$ don't know each other. Find the maximal number of people in that group, if we know that group doesn't have any $social$ nor $shy$ persons.
1. **Assume there are more than 40 people in the group.**
   - Let \( A \) be the person who has the most friends.
   - Let \( n \) be the number of friends of \( A \).
   - Let \( S \) be the subgraph which includes \( A \) and its friends.

2. **Case 1: \( n \geq 20 \)**
   - Let \( v_1, v_2, \ldots, v_n \) be the friends of \( A \).
   - Since \( A \) is not social, there is no edge between any \( v_i \) and \( v_j \).
   - If \( n \geq 21 \), then \( v_2, \ldots, v_{21} \) are not friends with \( v_1 \) and they are not friends with each other. So, \( v_1 \) is shy, which is a contradiction.
   - Therefore, \( n = 20 \).

3. **Let \( F \) be the subgraph which includes the vertices not in \( S \).**
   - \( F \) has at least 20 vertices.
   - \( A \) has no friends in \( F \), but \( A \) is not shy. So, \( F \) must be a complete graph.
   - Let \( B_1, B_2, \ldots, B_{20} \) be the people who are in \( F \).

4. **Lemma: Each \( B_i \) has at least 2 friends who are \( v_i \).**
   - Assume that \( B_1 \) is not friends with \( v_1, \ldots, v_{19} \).
   - Then \( B_1 \) is not friends with \( A, v_1, \ldots, v_{19} \). Also, \( v_1 \) and \( v_2 \) are not friends, so \( B_1 \) is shy, which is a contradiction.
   - Therefore, the lemma is true.

5. **Since \( B_1 \) is friends with \( B_2, \ldots, B_{20} \) and some \( v_i, v_j \), \( B \) has at least 21 friends, which gives a contradiction.**

6. **Case 2: \( n \leq 19 \)**
   - There are at least 21 people who are not in \( S \).
   - Let these people be \( k_1, k_2, \ldots, k_m \) with \( m \geq 21 \).
   - \( A \) is not friends with any \( k_i \), but \( A \) is not shy, which means \( k_1, k_2, \ldots, k_m \) form a complete graph, which gives a contradiction.

Therefore, the maximal number of people in the group is 40.

The final answer is \(\boxed{40}\).