#include <cstdio>

int main(void)
{
    long long n,a,b,c;

    scanf("%lld",&n);

    for(c = 1;c * c <= n;++c)
        if((n % c) == 0)
            a = n / c;

    b = 0;
    while(a)
        ++b,a /= 10;
    printf("%lld\n",b);
}
### Prompt

Generate a Cpp solution to the following problem:

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.

Examples

Input

10000


Output

3


Input

1000003


Output

7


Input

9876543210


Output

6

### Response

```cpp
#include <cstdio>

int main(void)
{
    long long n,a,b,c;

    scanf("%lld",&n);

    for(c = 1;c * c <= n;++c)
        if((n % c) == 0)
            a = n / c;

    b = 0;
    while(a)
        ++b,a /= 10;
    printf("%lld\n",b);
}
```