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"
)

const inf = 0x3f3f3f3f

func cal(n int) (ret int) {
	for n > 0 {
		ret++
		n /= 10
	}
	return ret
}

func main() {
	var n int
	fmt.Scanf("%d\n", &n)
	ans := inf
	for i := 1; i*i < n; i++ {
		if n%i != 0 {
			continue
		}
		j := n / i
		m1, m2 := cal(i), cal(j)
		if m2 > m1 {
			m1 = m2
		}
		if m1 < ans {
			ans = m1
		}
	}
	fmt.Printf("%d", ans)
}