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>
#define rep(i,n) for(i=0;i<n;i++)
int in_i(void){
	int i;
	scanf("%d",&i);
	return i;
}
long long in_ll(void){
	long long i;
	scanf("%d",&i);
	return i;
}
int cnt(long long a){
	int c=0;
	while(a){
		c++;
		a/=10;
	}
	return c;
}
int min(int a,int b){
	return a<b?a:b;
}
int max(int a,int b){
	return a>b?a:b;
}
int f(long long a,long long b){
	return max(cnt(a),cnt(b));
}
int main(void){
	long long n,i,ans=10;
	n=in_ll();
	for(i=1;i*i<=n;i++){
		if(n%i){
			continue;
		}
		ans=min(ans,f(i,n/i));
	}
	printf("%d\n",ans);
	return 0;
}