Subtract Digits to Reach Zero

At each step, choose a nonzero decimal digit currently present in the number and subtract that digit. Digits are taken from the new value after every step. Find the minimum number of steps needed to reach zero.

Implement removing_digits(n).

Input

n: The positive starting number.

Output

Return the fewest subtraction steps.

Constraints

1 ≤ n ≤ 1,000,000. Subtracting zero is not a useful move and is excluded.

Examples

Input:
n = 14

Expected output:
expected = 3

Input:
long long n = 14;

Expected output:
long long expected = 3;

Input:
long n = 14;

Expected output:
long expected = 3;

Input:
n = 7

Expected output:
expected = 1

Input:
long long n = 7;

Expected output:
long long expected = 1;

Input:
long n = 7;

Expected output:
long expected = 1;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Removing Digits — 1637