# Confusing Number

## Problem Description​

We can rotate digits by 180 degrees to form new digits. When 0, 1, 6, 8, 9 are rotated 180 degrees, they become 0, 1, 9, 8, 6 respectively. When 2, 3, 4, 5 and 7 are rotated 180 degrees, they become invalid.

A confusing number is a number that when rotated 180 degrees becomes a different number with each digit valid.(Note that the rotated number can be greater than the original number.)

Given a positive integer N, return the number of confusing numbers between 1 and N inclusive.

Example 1:

``Input: 20Output: 6Explanation: The confusing numbers are [6,9,10,16,18,19].6 converts to 9.9 converts to 6.10 converts to 01 which is just 1.16 converts to 91.18 converts to 81.19 converts to 61.``

Example 2:

``Input: 100Output: 19Explanation: The confusing numbers are [6,9,10,16,18,19,60,61,66,68,80,81,86,89,90,91,98,99,100].``

Note: `1 <= N <= 10^9`

``class Solution {    Map<Integer, Integer> map;    int count = 0;    public Solution() {        map = new HashMap<>();        map.put(6, 9);        map.put(9, 6);        map.put(0, 0);        map.put(1, 1);        map.put(8, 8);     }    private boolean isConfusingNumber(long n) {        long src = n;        long res = 0;        while (n > 0) {            res = res * 10 + map.get((int) n % 10);             n /= 10;        }        return res != src;    }    public int confusingNumberII(int N) {        for(int x: new int[]{1, 6, 8, 9}){            dfs(x, N);        }        return count;    }    public void dfs(long x, int N){        if(x>N) return;        if(isConfusingNumber(x)){            count++;        }        for(int y: new int[]{0, 1, 6, 8, 9}){            dfs(x*10 + y, N);        }    }}``