Write a program which computes the digit number of sum of two integers a and b.

Constraints

• 0 ≤ a, b ≤ 1,000,000
• The number of datasets ≤ 200

Input

There are several test cases. Each test case consists of two non-negative integers a and b which are separeted by a space in a line. The input terminates with EOF.

Output

Print the number of digits of a + b for each data set.

Example

Input

5 7
1 99
1000 999

Output

2
3
4

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