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 (3.4.3) (judge verdict: Wrong Answer)

import math
n = int(input())

a = 1
b = 1

'''
def get_prime(num):
    primes = {}
    origin_num = num
    primes[1] = 1

    tmp = int(math.sqrt(num) + 1)

    for i in range(2, tmp):
        while num % i == 0:
            num //= i

            if not (i in primes.keys()):
                primes[i] = 0
            primes[i] += 1

    if num != 1:
        primes[num] = 1

    if num == origin_num:
        primes[num] = 1

    return primes


prime_dic = get_prime(n)
prime_sorted = sorted(prime_dic.items(), key=lambda x: x[0], reverse=True)

for k, v in prime_sorted:
    for i in range(v):
        if a <= b:
            a *= k
        else:
            b *= k
'''


tmp = int(math.sqrt(n) + 1)

for i in range(1, tmp):
    if n % i == 0:
        a = i

b = int(n / a)

f = max(len(str(a)), len(str(b)))

print(f, a, b)