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 <algorithm>
#include <set>
#include <map>
#include <string>

using namespace std;
typedef long long ll;
#define rep(i,s,n)for(ll i = s;i<n;i++)
#define repe(i,s,n)for(ll i = s;i<=n;i++)
//ll p[1000000] = {};
ll dig(ll n) {
	//if (p[n] != 0) {
	//	return p[n];
	//}

	ll t = n;
	ll cnt = 0;
	while (t > 0) {
		t /= 10;
		cnt++;
	}
	//	p[n] = cnt;
	return cnt;
}
int main() {
	ll N; cin >> N;

	ll minV = 1 << 29;
	for (ll i = 1; i*i <= N; i++) {
		if (N % i == 0) {
			minV = min(minV, max(dig(i), dig(N / i)));
		}
	}
	cout << minV << endl;

	return 0;
}