You have been hired by a wearable technology startup to develop the core logic for a new digital smartwatch. The device's hardware tracks time in a single, continuous stream of total seconds elapsed since the start of the day. To make this data useful to the end-user, you must transform this raw integer into a standard human-readable digital clock format.

Methodology

To convert a large integer of seconds ($s$) into a structured time format, we follow a three-step mathematical breakdown using integer arithmetic:

Step 1: Extract Hours Calculate the total number of whole hours. Since there are $3600$ seconds in one hour, we divide the total seconds by $3600$.

$H = s // 3600$

Step 2: Extract Minutes Calculate the remaining seconds after hours are removed, then determine how many whole minutes are contained within that remainder.

$M = (s \pmod{3600}) // 60$

Step 3: Extract Seconds Determine the final remaining seconds that do not make up a full minute.

$S = s \pmod{60}$

Implementation

In Python, this logic is most efficiently implemented using Floor Division (//) to find whole units and the Modulo (%) operator to find the remainders. Once the numerical values are calculated, they must be formatted into a string. You should use f-strings with padding to ensure each unit (Hours, Minutes, Seconds) is always represented by two digits.

🛠️ System Note: This environment supports standard Python 3 formatting. You can use :02 within an f-string to automatically pad a single-digit number with a leading zero.

Consider the value 3661:

1. Hours: $3661 // 3600 = 1$
2. Minutes: $(3661(\mod 3600))//60=61//60=1$
3. Seconds: $3661(\mod60)=1$
4. Formatting: Results in "01:01:01"

Validation

To ensure your solution passes our automated verification system (==), you must perform the following formatting steps before returning your result:

1. Format: The output must be a string in the format HH:MM:SS.
2. Padding: Each unit must be exactly two digits. (e.g., 5 must be "05", 0 must be "00").

The Challenge

Implement the function format_duration(seconds). It must accept a non-negative integer and return the formatted "Digital Clock" string.

def format_duration(seconds):
    # Step 1: Calculate whole hours
    # Step 2: Calculate whole minutes from the remainder
    # Step 3: Calculate the final remaining seconds
    # Final Step: Return as a padded string "HH:MM:SS"
    pass