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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function Main(input){
	input=input.trim().split("\n");
	var N = parseInt(input,10);
	var rootN = Math.floor(Math.sqrt(N));
	var A;
	for (var i = rootN; i <= N; i++){
		if (N % i == 0){
			A = i;
			console.log(F(A));
			break;
		}	
    }
}

function F(x){
	var i = 1;
	var j = 1;
	while(true){
		j *= 10;
		if (x >= j){
			i++;
		} else {
			return i;
			break;
		}
	}
}	

Main(require("fs").readFileSync("/dev/stdin", "utf8"));