Takahashi has come to an integer shop to buy an integer.
The shop sells the integers from 1 through 10^9. The integer N is sold for $A \times N + B \times d(N) yen ($the currency of Japan), where d(N) is the number of digits in the decimal notation of N.
Find the largest integer that Takahashi can buy when he has X yen. If no integer can be bought, print 0.

-----Constraints-----
- All values in input are integers.
- $1 \leq A \leq 10^9$
- $1 \leq B \leq 10^9$
- $1 \leq X \leq 10^{18}$

-----Input-----
Input is given from Standard Input in the following format:
A B X

-----Output-----
Print the greatest integer that Takahashi can buy. If no integer can be bought, print 0.

-----Sample Input-----
10 7 100

-----Sample Output-----
9

The integer 9 is sold for $10 \times 9 + 7 \times 1 = 97$ yen, and this is the greatest integer that can be bought.
Some of the other integers are sold for the following prices:
- 10: $10 \times 10 + 7 \times 2 = 114$ yen
- 100: $10 \times 100 + 7 \times 3 = 1021$ yen
- 12345: $10 \times 12345 + 7 \times 5 = 123485$ yen

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