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: Accepted)

'use strict'
function main(input) {
  const N = parseInt(input, 10);

  let maxB = 0;
  for (let A = 1; A < N; A++) {
    let B = N / A;
    if (Number.isInteger(B)) {
      maxB = B;
    }
    if (A > B) {
      break;
    }
  }

  const digit = maxB.toString().length;
  console.log(digit);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));