Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
int keta(int);
int main(void)
{
int N;
int a,b,min;

scanf("%d", &N);

a=(int)sqrt(N);
while(a!=0){
b=(int)N/a;
while(b*a!=N){
b++;
if(b*a>N){
break;
}
}
if(a*b==N){
break;
}
a--;
}

if(a>b)
printf("%d\n", keta(a));
else
printf("%d\n", keta(b));

return 0;
}

int keta(int x)
{
int c=0;
while(x>0){
c++;
x/=10;
}
return c;
}