Problem:
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

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

Solution in Ruby (judge verdict: Accepted)

def digit(n)
  if n < 10
    return 1
  else
    return digit(n / 10) + 1
  end
end
while (str = gets)
  puts digit(str.split(" ").inject(0){|sum,i|sum + i.to_i})
end