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 main() {
        var n int
        fmt.Scan(&n)
        l := int(math.Sqrt(float64(n)))
        min := math.MaxInt32
        for i := 1; i <= l; i++ {
                if n%i == 0 {
                        var cmin int
                        if di, dni := digits(i), digits(n/i); di < dni {
                                cmin = dni
                        } else {
                                cmin = di
                        }
                        if cmin < min {
                                min = cmin
                        }
                }
        }
        fmt.Printf("%d\n", min)
}

func digits(n int) (d int) {
        tmp := n
        for tmp > 0 {
                d++
                tmp /= 10
        }
        return d
}