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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func divs(n int) []int {
	r := make([]int, 0)
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			r = append(r, i)
			if i*i != n {
				r = append(r, n/i)
			}
		}
	}
	return r
}
func cols(n int) int {
	cnt := 0
	for n > 0 {
		cnt++
		n /= 10
	}
	return cnt
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func main() {
	var N int
	fmt.Scan(&N)
	ds := divs(N)
	ans := int(1e10) + 1
	for _, v := range ds {
		ans = min(ans, max(cols(v), cols(N/v)))
	}
	fmt.Println(ans)
}