After robbing those houses on that street, the thief has found himself a new place for his thievery so that he will not get too much attention. This time, all houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, the security system for these houses remain the same as for those in the previous street.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

class Solution {
    public int rob(int[] nums) {
        int n = nums.length;
        if (n == 0) {return 0;}
        if (n == 1) {return nums[0];}
        if (n == 2) {return Math.max(nums[0],nums[1]);}
        
        int[] dp = new int[n+1];
        //no 1
        dp[0] = 0;
        dp[1] = 0;
        for (int i = 2; i <= n; i++){
            dp[i] = Math.max(dp[i-1], dp[i-2]+nums[i-1]);
        }
        
        int flag1 = dp[n];
        
        dp[0] = 0;
        dp[1] = nums[0];
        
        for (int i = 2; i < n; i++){
            dp[i] = Math.max(dp[i-1], dp[i-2]+nums[i-1]);
        }
          
        int flag2 = dp[n-1];
        
        return Math.max(flag1, flag2);
    }
}