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)

import sys
from collections import deque
from itertools import *


def I(): return int(sys.stdin.readline().rstrip())


def LI(): return list(map(int, sys.stdin.readline().rstrip().split()))


def S(): return sys.stdin.readline().rstrip()


def LS(): return list(sys.stdin.readline().rstrip().split())


def make_divisors(n):
    lower_divisors, upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]


N = I()
ans_list = []
divi_list = make_divisors(N)

for i in range(len(divi_list)):
    for q in range(len(divi_list)):
        if divi_list[i] * divi_list[q] == N:
            ans_list.append(
                max(len(str(divi_list[i])), len(str(divi_list[q]))))
print(min(ans_list))