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)

# AOJ 0002 Digit Number

sums = ARGF.each_line.map {|line| line.split(" ").map {|x| x.to_i} \
                           .reduce(0, :+)}
sums.map {|s|
  if s.zero?
    1
  else
    Math.log10(s).to_i + 1
  end
}.each {|d| puts d}