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 PyPy3 (2.4.0) (judge verdict: Accepted)

def make_divisors(n):
    divisors = []
    min_k = 10
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            k = max(len(str(int(i))), len(str(int(n // i))))
            min_k = min(min_k, k)

    # divisors.sort()
    return min_k

N = int(input())
# min_k = len(str(N)) + 1
# for i in range(1, N):
#     if N % i != 0:
#         continue
#     if i ** 2 > N:
#         break
#     else:
#         ii = N // i
#         k = max(len(str(i)), len(str(ii)))
#         # print(i, ii, k, min_k)
#         if min_k > k:
#             min_k = k
print(make_divisors(N))