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 <map>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#define REP(i, n) for(int i = 0; i < n; ++i)
#define RANGE(i, x, n) for(int i = x; i < n; ++i)

using namespace std;

typedef long long ll;
const int INF = 0x3f3f3f3f;

int main()
{
    ll N;
    cin >> N;
    int ans = INF;
    RANGE(i, 1, sqrt(N) + 1) {
        if(N % i == 0) {
            ll y = N / i;
            ans = min(ans, max((int)to_string(y).size(), (int)to_string(i).size()));
        }
    }
    cout << ans << endl;
}