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>
#include<string.h>
int main(){
	int n;
	int a,b;
	int ma,mb;
	scanf("%d",&n);
    int i;
    for(i=1;i<=sqrt(n);i++){
    	if(n%i==0){
    		a=i;
    		b=n/i;
		}
	}
	for(i=0;;i++){
		if(a%(int)pow(10,i)==a){
			ma=i;
			break;
		}
	}
	for(i=0;;i++){
		if(b%(int)pow(10,i)==b){
			mb=i;
			break;
		}
	}
	if(ma>=mb){
		printf("%d\n",ma);
	}else{
		printf("%d\n",mb);
	}
	return 0;
}