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 (
  "fmt"
  "math"
  "strconv"
)
func main() {
  var n,m,h,l int64
  fmt.Scan(&n)
  m = sqrt(n)
  h = n/2 + 1
  l = 0
  for i:=m;i<h;i++ {
    if n%i == 0 {
      l = i
      break
    }
  }
  if l == 0 {
    fmt.Println(len(strconv.FormatInt(n,10)))
  } else {
    fmt.Println(len(strconv.FormatInt(l,10)))
  }
}
func sqrt(n int64) int64 {
  var f float64 = math.Sqrt(float64(n))
  return int64(math.Ceil(f))
}