Facebook | Phone | Count All Friend Requests

A group of centaurs (mythical half-human, half-horse creatures) all sign up for Facebook accounts at the same time. They immediately start sending each other friend requests, in accordance with the ancient rules that have governed centaur friendship since the dawn of time:

1. A centaur will only send a friend request to another centaur if the recipient is at least (X/2 + 7) of the sender's age. For example, a 200-year old centaur can only send friend requests to centaurs that are at least 107 years old.
2. A centaur will not send a friend request to another centaur that is older than it is.
3. A centaur over 100 years old will not send a friend request to a recipient under 100 years old. But centaurs under 100 years old can friend each other.
4. If any of the conditions for sending a friend request are not met, no friend request will be sent.

Write a function that, given an array of centaur ages, returns an integer of the total number of friend requests that the group of centaurs will send to each other.

Examples:

count_all_friend_requests([120, 110])  => 1
Friend requests             1    0
count_all_friend_requests([120, 110, 99]) => 1
Friend requests             1    0    0
count_all_friend_requests([120, 45, 230, 400, 88, 300, 101]) => 4
Friend requests             1    0   0    2    0   1    0
count_all_friend_requests([120, 45, 55, 230, 400, 88, 300, 101]) => 6
Friend requests             1    0   1   0    2    1   1    0