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"
	"math"
)

func f(x int) int {
	ret := 0
	for 0 < x {
		x /= 10
		ret++
	}
	return ret
}

func main() {
	var n float64
	fmt.Scan(&n)
	wareru := 0
	for i := 1.0; i <= math.Sqrt(n); i += 1.0 {
		if int(n)%int(i) == 0 {
			wareru = int(i)
		}
	}
	b := int(n) / wareru
	// それぞれの桁数を比較して大きい方
	aketa, bketa := f(wareru), f(b)
	fmt.Println(int(math.Max(float64(aketa), float64(bketa))))
}