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)

def digits(n)
    return 1 if n < 10
    1 + digits(n/10)
end

while true
    line = gets
    break if not line
    
    d = line.chomp.split(" ").map &:to_i
    puts digits(d[0]+d[1])
end