Numbers

Your task is to count how many numbers in the range $[a,b]$ consist of the digits $2$ and $5$ only. For example, in the range $[1,100]$ the numbers are $2$, $5$, $22$, $25$, $52$ and $55$, and thus the answer is $6$.

In a file twodigit.py, implement the function count_numbers that counts the desired numbers in the range. The function is given the parameters $a$ and $b$ representing the end points of the range.

Your function will be tested using many different ranges. In each test, $1 \le a \le b \le 10^9$.

You must implement the function efficiently so that the solution is returned quickly even for long ranges.

def count_numbers(a, b):
    # TODO

if __name__ == "__main__":
    print(count_numbers(1, 100)) # 6
    print(count_numbers(60, 70)) # 0
    print(count_numbers(25, 25)) # 1
    print(count_numbers(1, 10**9)) # 1022
    print(count_numbers(123456789, 987654321)) # 512