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;
#define REP(i,n) for(ll i=0, i##_len=(n); i<i##_len; ++i)
#define REPR(i,n) for(ll i = n;i >= 0;--i)
#define FOR(i,m,n) for(ll i = m, i##_len=(n);i <i##_len; ++i)
#define all(x) (x).begin(),(x).end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
const int INF = 1e9;
const ll LLINF = 1e16;

ll modinv(ll a, ll m) {
    ll b = m, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}


ll divisormax_min(ll n)
{
    ll ans = LLINF;
    for(ll i = 1;i*i<= n;i++){
        if(n%i == 0){
            ans = log10(n/i)+1;
        }
    }
    return ans;
}

int main(void)
{
    ll n;
    cin >> n;
    ll ans = divisormax_min(n);
    cout << ans << endl;

    return 0;
}