X is a good number if after rotating each digit individually by 180 degrees, we get a valid number that is different from X. Each digit must be rotated - we cannot choose to leave it alone.

A number is valid if each digit remains a digit after rotation. 0, 1, and 8 rotate to themselves; 2 and 5 rotate to each other (on this case they are rotated in a different direction, in other words 2 or 5 gets mirrored); 6 and 9 rotate to each other, and the rest of the numbers do not rotate to any other number and become invalid.

Now given a positive number `N`

, how many numbers X from `1`

to `N`

are good?

Example:Input:10Output:4Explanation:There are four good numbers in the range [1, 10] : 2, 5, 6, 9. Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.

**Note:**

- N will be in range
`[1, 10000]`

.

```
struct Solution;
#[derive(Debug, PartialEq, Eq, Clone, Copy)]
enum D {
Invalid,
Same,
Different,
}
impl D {
fn new(d: usize) -> Self {
match d {
0 | 1 | 8 => D::Same,
2 | 5 | 6 | 9 => D::Different,
_ => D::Invalid,
}
}
}
impl Solution {
fn rotated_digits(n: i32) -> i32 {
let n: usize = n as usize;
let mut a: Vec<D> = vec![D::Invalid; (n + 1) as usize];
for i in 0..=n {
if i < 10 {
a[i] = D::new(i);
} else {
let j = i / 10;
let k = i % 10;
a[i] = match (a[j], a[k]) {
(D::Invalid, _) => D::Invalid,
(_, D::Invalid) => D::Invalid,
(D::Different, _) => D::Different,
(_, D::Different) => D::Different,
(D::Same, D::Same) => D::Same,
}
}
}
a.iter()
.fold(0, |sum, &d| if d == D::Different { sum + 1 } else { sum })
}
}
#[test]
fn test() {
assert_eq!(Solution::rotated_digits(10), 4);
}
```