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)

a = 0
b = 0

while ( a != nil && b != nil)

  a, b = gets.to_i, gets.to_i

  x = a + b
  res = 0

  while x != 0
    x /= 10
    res += 1
  end

  puts res
end