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: Accepted)

#include<stdio.h>
#include<math.h>
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define abs(a) ((a)>0 ? (a):-(a))
#define ll long long

int main(){
	ll n,small =10000000000;
	int ans = 0ll;

	scanf("%lld",&n);

	if(n == 1 || n == 2){
		printf("1\n");
		return 0;
	}
	if(n == 3){
		printf("1\n");
		return 0;
	}
	FOR(i,1,sqrt(n)+1){
		if(n % i == 0){
			if(small > (i>n/i ? i:n/i)) small = (i>n/i ? i:n/i);
		}
	}

	//printf("%lld\n",small);


	FOR(i,1,12){
		if(small < pow(10,i)){
			ans = i;
			break;
		}
	}

	printf("%d\n",ans);
}