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 Python (3.8.2) (judge verdict: Accepted)

def calc_digits(num):
    ans = 1
    while True:
        if num // 10 == 0:
            break
        num //= 10
        ans += 1

    return ans


def main():
    N = int(input())
    ans = 10 ** 10

    for A in range(1, int(N ** 0.5) + 1):
        if N % A != 0:
            continue
        B = N // A
        A_digits = calc_digits(A)
        B_digits = calc_digits(B)

        max_digits = max(A_digits, B_digits)
        if max_digits < ans:
            ans = max_digits

    print(ans)


if __name__ == "__main__":
    main()