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: Runtime Error)

import math
import sys
n = int(input())

insu = {}

sq = math.ceil(math.sqrt(n))
for i in range(1, sq + 1):
    if n % i == 0:
        insu[i] = 1
        insu[n // i] = 1

dct = sorted(insu.items())

for i in range(len(dct) // 2 + 1):
    if len(dct) - i * 2 <= 1:
        ans1 = dct[i][0]
        ans2 = dct[len(dct) - i][0]
        for i in range(1, 10):
            if ans2 // 10 == 0:
                print(i)
                break
            ans2 //= 10
        sys.exit(0)