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 "bits/stdc++.h"

#define fi first
#define se second
#define all(x) x.begin(), x.end()
using namespace std;
using ull = unsigned long long;
using ll = long long;
constexpr int I_INF = INT_MAX;
constexpr ll L_INF = LLONG_MAX;
const long double PI = (acos(-1));
const ull MOD = 1000000007;


struct __INIT {
    __INIT() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} __init;

int main(){
    ll N;
    cin >> N;
    ll min_f = 10;
    for(ll A = 1; A <= pow(N, 0.5); A++){
        if(N % A == 0) min_f = min(min_f, (ll)max(to_string(A).size(), to_string(N / A).size()));
    }
    cout << min_f << endl;
}