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>
using namespace std;
 
typedef long long ll;
typedef pair<int,int> P;
 
const int INF = 1e9;
const int mod = 1e9+7;
 
int cal(ll z)
{
    int cnt;
    for(cnt = 0; z != 0; cnt++) z /= 10;
    return cnt;
}

int main()
{
    ll n;
    cin >> n;
    int ans = INF;
    for(ll i = 1; i*i <= n; i++){
        if(n%i == 0){
            int a = cal(i),b = cal(n/i);
            ans = min(ans,max(a,b));
        }
    }
    cout << ans << endl;
    return 0;
}