KöMaL 2019 B5014

After the elections in Nowhereland, there are $50 < n < 100$ representatives in the parliament, all from a single party called the Blue Party. (The Blue Party has a single president.) According to the law, a party in the parliament may be divided into two parties as long as the following conditions are met:

• The president of the old party is not allowed to become a member of the newly formed parties. His or her parliament mandate will terminate, thereby reducing the total number of representatives.
• Every other member may decide which new party to join.
• Each of the new parties must have at least one member among the representatives.
• Each of the new parties must elect a president from their representatives. If at least one such splitting of a party results in all parties in the parliament having the same number of members, the parliament will be dissolved. What should be the value of $n$ so that this could never happen?