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: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

func main() {
	N := nextInt()

	min := int(math.Pow10(10))
	digit := 0
	for i := 2; i < N; i++ {
		if N%i == 0 {
			v := N / i
			num := max(v, i)
			if num < min {
				min = num
				digit = len(fmt.Sprint(num))
			}
		}
	}

	if digit == 0 {
		fmt.Println(len(fmt.Sprint(N)))
		return
	}

	fmt.Println(digit)
}

// Input. ----------

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Buffer([]byte{}, math.MaxInt64)
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}

	return i
}

func nextString() string {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}

	return sc.Text()
}

// ---------- Input.

// Util. ----------

func min(x, y int) int {
	if x < y {
		return x
	}

	return y
}

func max(x, y int) int {
	if x > y {
		return x
	}

	return y
}

// ---------- Util.