Problem Description

You are given an array ages, where ages[i] represents the age of the i-th person. A person of age A will send a friend request to a person of age B if and only if all of the following conditions are met:

1. B > 0.5 * A + 7
2. B <= A

Each request is directed (A → B). A person cannot send a request to themselves. This means if there are multiple people of the same age, they can send requests to each other, but a single individual cannot send a request to themselves.

Return the total number of friend requests that will be sent.

Input

• ages: An integer array where ages[i] is the age of the i-th person.

Output

• An integer representing the total number of directed friend requests.

Constraints

• 1 <= n <= 2 * 10^4, where n is the number of people (length of the ages array).
• 1 <= ages[i] <= 120, where ages[i] is the age of a person.

Examples

Example 1:

ages = [16, 16]

• A person of age 16 can send a request to another person of age 16 because:
  • 16 > 0.5 * 16 + 7 (which is 16 > 8 + 7 = 15) - True
  • 16 <= 16 - True
• Since there are two distinct 16-year-olds, the first can request the second, and the second can request the first.
• Total = 2

Example 2:

ages = [20, 30, 100, 110, 120]

• The total number of directed requests satisfying the rules needs to be computed.