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: Time Limit Exceeded)

while line = gets do
  sum = 0
  a,b = line.split.map(&:to_i)
  sum = a + b
  digit = 0
  while
    digit += 1
    if 10**(digit - 1) < sum && 10**(digit) - 1 > sum
      puts digit
      break
    end
  end
end