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)

#include <bits/stdc++.h>
#define rep(i, n) for(long long i = 0; i < (n); i++)
using namespace std;

long long f(long long x)
{
	long long ans, i = 1;

	while (i * i <= x)
	{
		if (x % i == 0)
			ans = i;
		i++;
	}
	return ans;
}

signed main(void)
{
	long long n, x, y, ans1, ans2;
	cin >> n;
	x = f(n);
	y = n / x;
	ans1 = ans2 = 0;
	while(x)
	{
		ans1++;
		x /= 10;
	}
	while (y)
	{
		ans2++;
		y /= 10;
	}
	cout << max(ans1, ans2) << endl;
	return 0; 
}