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>
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;

int main()
{
    ll ans=1;
    int march[5]={0};
    int n,sum=0,el=0;
    scanf("%d",&n);
    char s[15];
    rep(i,n){
        scanf("%s",s);
        switch(s[0]){
            case 'M': march[0]++; break;
            case 'A': march[1]++; break;
            case 'R': march[2]++; break;
            case 'C': march[3]++; break;
            case 'H': march[4]++; break;
            default : break;
        }
    }
    
    for(int i=0;i<3;i++){
        for(int j=i+1;j<4;j++){
            for(int k=j+1;k<5;k++){
                ans+=march[i]*march[j]*march[k];
            }
        }
    }
    printf("%lld",ans);
}