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<cstdio>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<string>
#include<stack>
#include<queue>
#include<vector>
#include<map>
#define fi first
#define se second
#define pb(i) push_back(i)
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define per(i,a,b) for(int i=a;i>=b;i--)
#define mes(a,b) memset(a,b,sizeof(a))
#define sbs(i,j) substr(i,j)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N = 1e6+10;
const int INF = 0x3f3f3f3f;
const int inf = - INF;
const int mod = 1e9+7;
const double pi = acos(-1.0);

int get_digits(int x){
    int cnt=0;
    while(x){
        cnt++;
        x/=10;
    }
    return cnt;
}
int main(){
    ll N;
    cin>>N;
    int ans=get_digits(N);
    for(ll i = 1;i*i<=N;i++){
        if(N%i!=0) continue;
        ll k=N/i;
        ans=min(ans,max(get_digits(k),get_digits(i)));
    }
    cout<<ans<<endl;
    getchar();
    return 0;
}