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 func(int a,int b){
    int n=0,m=0;
    while(a>0){
        n++;
        a/=10;
    }
    while(b>0){
        m++;
        b/=10;
    }
    int ans=n;
    if(n<m){ans=m;}
    return ans;
}
int main(void){
    int a,b,n,m,answ;
    long long int N;
    scanf("%lld",&N);
    answ=func(1,N);
    for(int i=2;i<pow(N,0.5);i++){
        if(N%i==0){
        if(answ>func(i,N/i)){answ=func(i,N/i);}
    }}
    printf("%d\n",answ);
    return 0;
}