import math
 
FUEL_PER_MILE = 2.125
 
# Function to check if a number is an odd prime
def is_odd_prime(n):
    if n < 2 or n % 2 == 0:
        return False
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        if n % i == 0:
            return False
    return True
 
# Function to simulate the trip
def simulate_trip(initial_fuel, print_output=False):
    fuel = initial_fuel
    location = 0
 
    while fuel >= 0:
        if print_output:
            print("LOCATION: {:<2}    FUEL: {:<.6f}".format(location, fuel))
 
        fuel -= FUEL_PER_MILE  # Consume fuel per mile
        if print_output:
            print("{:.3f} FUEL BURNED".format(FUEL_PER_MILE))
 
        if is_odd_prime(location):
            fuel += location  # Add fuel at odd prime mile markers
            if print_output:
                print("{} FUEL ADDED AT ODD PRIME MILE MARKER".format(location))
 
        if fuel < 0:
            return location + (fuel / FUEL_PER_MILE)  # Exact stranded location
 
        location += 1
 
    return float('inf')  # If never stranded, return infinity
 
# Minimum fuel needed to never get stranded
min_fuel = 7.0  # Starting with 7.0 units of fuel
 
# Verify if 7.0 is enough
result = simulate_trip(min_fuel, print_output=True)
 
if result == float('inf'):
    print("Minimum starting fuel: {:.6f}".format(min_fuel))
else:
    print("ERROR: 7.0 is not enough fuel!")
 
# Part 2: Simulate with one drop less fuel
stranded_location = simulate_trip(min_fuel - 0.0001, print_output=True)
print("FINAL STRANDED LOCATION: {:.7f}".format(stranded_location))
 

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