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<iostream>
#include<string>
#include<algorithm>
#include<math.h>
#include<queue>
#define ll long long
const int MOD= 1e9 + 7;
const int INF = 1000000005;
using namespace std;

int check(ll x) {
	int ret = 0;
	while (x != 0) {
		x /= 10;
		ret++;
	}
	return ret;
}

int main()
{
	ll n;
	cin >> n;
	int a, b, ans = INF;
	for (ll i = 1; i <= sqrt(n); i++) {
		if (n == (n / i)*i) {
			a = check(i);
			b = check(n / i);
			ans = min(ans, max(a,b));
		}
	}
	cout << ans << endl;
	return 0;

}