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)

gets.each_line do |line|
	num = line.split(" ")
	sum = 0
	num.each{|n| sum += n.to_i}
	cnt = 0
	while sum > 0 do
		sum=sum/10
		cnt+=1
	end
	p cnt
end