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 Python3 (judge verdict: Wrong Answer)

import math
import sys

for line in sys.stdin:
    words=line.strip().split(" ")
    a=int(words[0])
    b=int(words[1])
    if a==0 and b==0:
        print(2)
    else:
        if a==0:
            a=1
        else:
            a = int(1.0+math.log(a,10))
        if b==0:
            b=1
        else:
            b = int(1.0+math.log(b,10))
        print(a+b)