Given an integer
N (
\(1<=N<=10^{10}\)).
Given two positive integers
A and
B , define
\(F (A, B)\) as the larger of the two:
- number of digits in decimal notation
A;
- number of digits in the decimal representation of the number
B.
For example,
\(F (3,11) = 2\) because 3 is one digit and 11 is two.
Find the minimum value of
\(F (A, B)\) among all pairs of positive integers
A and
B such that \(N = A \cdot B\).
Input
The input is an integer N (\(1<=N<=10^{10}\)).
Imprint
Display the answer to the problem.
Examples
| # |
Input |
Output |
Explanation |
| 1 |
10000 |
3 |
\(F(A,B) \) has a minimum value when \((A,B )=(100,100)\). |
| 2 |
1000003 |
7 |
There are two pairs A and B, so that the condition of the problem is fulfilled: \((1, 1000003)\) and \((1000003,1)\). For these pairs, \(F(1,1000003)=F(1000003,1)=7\). |
| 3 |
9876543210 |
6 |
|