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: Wrong Answer)

#!/usr/local/bin/ruby
while line=gets
   rec=line.split(" ").map(&:to_i)
   x,y=rec[0],rec[1]
   ans = x + y
   if 0 < ans and ans < 10
      puts "1"
   elsif 10 <= ans and ans < 100
      puts "2"
   elsif 100 <= ans and ans < 1000
      puts"3"
   elsif 1000 <= ans and ans < 10000
      puts"4"
   elsif 10000 <= ans and ans < 100000
      puts"5"
   elsif 100000 <= ans and ans <= 2000000
      puts"6"
   end
 end