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++14 (GCC 5.4.1) (judge verdict: Accepted)

// ABC057
#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>

#define INF 1000000000

using namespace std;

int nd(int a)
{
    int n = 0;
    while (1)
    {
        n++;
        a /= 10;
        if(a == 0) break;
    }

    return n;
}

int f(int a, int b)
{
    return max(nd(a), nd(b));
}


int main()
{
    long long n;
    cin >> n;
    int div;

    for(int i = sqrt(n); i >= 1; i--)
    {
        if(n % i == 0)
        {
            div = i;
            break;
        }
    }

    cout << f(div, n/div) << endl;

    return 0;
}