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 <iomanip>
#include <string>
#include <string.h>
#include <math.h>
#include <cmath>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <algorithm>
#include <utility>
#include <deque>
#include <queue>
#include <functional>

#define rep(i, n) for(int i = 0; i < n; ++i)
#define REP(i, m, n) for(int i = m; i < n; ++i)
#define rrep(i,n) for(int i = n; i >= 0; --i)
#define RREP(i, m, n) for(int i = n; i >= m; --i)
#define llrep(i, n) for(ll i = 0; i < n; ++i)
#define llREP(i, m, n) for(ll i = m; i < n; ++i)
#define llrrep(i,n) for(ll i = n; i >= 0; --i)
#define llRREP(i, m, n) for(ll i = n; i >= m; --i)

using ll = long long;
using ull = unsigned long long;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
using pli = std::pair<long long, int>;
using plpii = std::pair<long long, std::pair<int, int>>;
using pdd = std::pair<double, double>;

using namespace std;

const long long _MOD = 1000000007;
const long long MOD = 998244353;
const int ALPHABET = 27;
const double pi = 3.14159265358979;

int f(ll a, ll b) {
	if (b > a) swap(a, b);

	int rtv = 0;
	while (a > 0) {
		a /= 10;
		++rtv;
	}

	return rtv;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	ll n;
	cin >> n;
	int ans = _MOD;
	for (ll i = 1; i*i <= n; ++i) {
		if (n%i == 0) {
			ans = min(ans, f(i, n / i));
		}
	}

	cout << ans << "\n";

	return 0;
}