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)

while data = gets
  sum = data.chomp.split(" ").map(&:to_i).inject(&:+)
  digit = 0
  if sum == 0
    puts 1
  else
    until sum == 0
      sum /= 10
      digit += 1
    end
    puts digit
  end
end