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>

using namespace std;
using ll = long long;

// 桁数を求める
int cnt_dig(ll num) {
    int cnt = 0;
    while(num > 0) {
        num /= 10;
        cnt++;
    }

    return cnt;
}

int main() {
    ll N;
    cin >> N;

    // 最大公約数を求める
    ll tmp_m = 0;
    ll ans = cnt_dig(N);

    for(ll i = 1ll; (i * i) < N; ++i) {
        if (N%i != 0) continue;
        const ll B = N / i;

        const int tmp_m = max(cnt_dig(i), cnt_dig(B));

        if (tmp_m < ans) {
            ans = tmp_m;
        }
    }

    cout << ans << endl;
    return 0;
}