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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

func getAnswer(a, b int) int {
	A := getDigit(a)
	B := getDigit(b)
	if A > B {
		return A
	} else {
		return B
	}
}

func getDigit(num int) int {
	i := 1
	for {
		if num < 9 {
			break
		}
		num = num / 10
		i += 1
	}
	return i
}

var N int

func main() {
	fmt.Scan(&N)
	hoge := int(math.Sqrt(float64(N)))
	for i := hoge; i > 0; i-- {
		if N%i == 0 {
			fmt.Println(getAnswer(hoge, N/hoge))
			break
		}
	}
}