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 a(long long b);

int main(void){
    long long n, n2;
    int i, j, min, ans;
    scanf("%lld", &n);
    n2 = sqrt(n);
    min = n2;
    for(i=1; i<n2; i++){
        if(n%i == 0){
            long long b = n / i;
            ans = a(b);
            if(ans<min){
                min = ans;
            }
        }
    }
    printf("%d\n", min);
    return 0;
}

int a(long long b){
    int t;
    if(b==0){ return 0; }
    else{ 
        b /= 10;
        t = 1 + a(b);
    }
    return t;
}