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



Sample input:
10000


Sample output:
3

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3


def div_pairs(n):
    for i in range(1, n):
        if i * i > n:
            break
        d, m = divmod(n, i)
        if m == 0:
            yield (i, d)


def f(a, b):
    return max(len(str(a)), len(str(b)))


def solve(n):
    return min(f(a, b) for a, b in div_pairs(n))


def main():
    print(solve(int(input())))


if __name__ == '__main__':
    main()