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: Wrong Answer)

#include<bits/stdc++.h>
constexpr long long INFL = 1LL << 60;
constexpr int INF = 1 << 30;

using namespace std;

using ll = long long;
using P = tuple<int, int>;
using iarr = valarray<int>;

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

    int min_length = INF;
    for(ll i = 1; i < N; ++i){
        if(i*i > N) break;
        if(N % i == 0){
            string s1 = to_string(i);
            string s2 = to_string(N/i);
            int f = max(s1.size(), s2.size());
            min_length = min(f, min_length);
        }
    }
    cout << min_length << endl;
    return 0;
}