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<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<map>
#include<utility>
#include<set>
#include<stack>
#include<queue>
#include<deque>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<bitset>
#include<sstream>
#include<list>
#include<climits>

using namespace std;
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define nrep(i,i0,n) for(int i=(i0);i<(int)(n);++i)
typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii;
typedef vector<vector<int> > vii;
typedef long long ll;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	ll n;cin>>n;
	int minj=10;
	nrep(i,1,(int)sqrt(n)){
		if(n%i==0){
			ll t=n/i;
			int tmp=(int)log10(1.0*t)+1;
			minj=min(minj,tmp);
		}
	}
	cout<<minj<<endl;
	return 0;
}