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>

long int F_func(long int a, long int b) {
    long int c=0;
    if(a>b) {
        while(a) {
            c += 1;
            a /= 10;
        }
    } else {
        while(b) {
            c += 1;
            b /= 10;
        }
    }
    return c;
}

int main() {
    long int n;
    scanf("%ld", &n);

    long int flag=1, tmp, min=100;
    while(n>=flag*flag) {
        if(n%flag==0) {
            tmp = F_func(flag, n/flag);
            if(min>tmp) {
                min = tmp;
            }
        }
        flag++;
    }

    printf("%ld\n", min);

    return 0;

}