Digit Number

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

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.

Constraints

0 ≤ a , b ≤ 1,000,000

, ≤ 1,000,000 The number of datasets ≤ 200

Output

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

Sample Input

5 7 1 99 1000 999

Output for the Sample Input

2 3 4