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)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

import math


def division(n):
    r, cur, ans = math.floor(math.sqrt(n)), 2, []

    while cur <= r:
        while n % cur == 0:
            ans.append(cur)
            n /= cur
        cur += 1
    return ans + [int(n)]


def f(ret):
    l, r = 1, 1
    for n in reversed(ret):
        if l < r:
            l *= n
        else:
            r *= n

    return max(len(str(l)), len(str(r)))


ret = division(int(input()))
print(f(ret))