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>

using namespace std;

using ll = long long;

const long long MOD = 1e9 + 7;
const int INF = 1e9 + 7;

int F(long long x) {
    int res = 0;
    while (x > 0) x /= 10, res++;
    return res;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    long long N;
    cin >> N;
    int ans = INF;
    for (long long i = 1; i * i < N; ++i) {
        if (N % i != 0) continue;
        long long A, B;
        A = i;
        B = N / i;
        int f = max(F(A), F(B));
        ans = min(ans, f);
    }
    cout << ans << endl;
}