Group Birthdays

Computes a single birthday for a group of persons that have different birthdays

A group of persons (let's say a family) may be interested to have a single day in a year when they all come together to celebrate their birthdays as a group, the program computes what this day should be. The computation is done in a manner quite similar to taking the arithmetic averages of the birthdays of individuals in the group.
The user should enter the celebration year and the birthdays of the individuals in the group as explained within the program file. The user should not modify the part of the program below where it is clearly written "DO NOT MODIFY"