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>
#include<iomanip>
using namespace std;
using ll =  long long;
#define REP(i, n) for(int i=0; i<(n); ++i)
#define FOR(i, a, b) for(int i=(a); i<(b); ++i)
#define FORR(i, a, b) for(int i=(b)-1; i>=(a); --i)
vector<ll> prime(ll n){
    vector<ll> p;
    for(ll i=2LL;i<=sqrt(n)+2;++i){
        while(n%i == 0){
            n/=i;
        p.push_back(i);
                    }
    }
    if(n > 1)p.push_back(n);
    return p;
}
int hoge(ll a){
    int num =0;
    while(a >0){
        a /= 10;
        num++;
    }
    return num;
}
ll MOD=1e9+7;
int main() {
    ll n;
    cin>>n;
    auto v = prime(n);
    ll a,b;
    a=b=1LL;
    int ret = 40;
    for(int i=0;i<(int)v.size();++i){
        b = 1LL;
        for(int j=i;j<(int)v.size();++j){
            b *= v[j];
        }
        ret = min(ret,max(hoge(a),hoge(b)));
        a *= v[i];
    }
    cout << ret << endl;
    return 0;
}