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 <vector>
#include <map>
#include <cmath>

using namespace std;

int main() {
    long long N;
    cin >> N;

    long long sqrtNp1 = 1 + (long long)sqrt(N);
    long long ans = 10;
    for (long long i = 1; i < sqrtNp1; ++i) {
        if (N % i == 0) {
            long long A = i;
            long long B = N / i;
            long long ndigitA = 1 + (long long)log10l(A);
            long long ndigitB = 1 + (long long)log10l(B);
            long long F = max(ndigitA, ndigitB);
            if (F < ans) {
                ans = F;
            }
        }
    }

    cout << ans << endl;
    return 0;
}