<p>You may recall that an array <code>arr</code> is a <strong>mountain array</strong> if and only if:</p>

<ul>
	<li><code>arr.length &gt;= 3</code></li>
	<li>There exists some index <code>i</code> (<strong>0-indexed</strong>) with <code>0 &lt; i &lt; arr.length - 1</code> such that:
	<ul>
		<li><code>arr[0] &lt; arr[1] &lt; ... &lt; arr[i - 1] &lt; arr[i]</code></li>
		<li><code>arr[i] &gt; arr[i + 1] &gt; ... &gt; arr[arr.length - 1]</code></li>
	</ul>
	</li>
</ul>

<p>Given an integer array <code>nums</code>​​​, return <em>the <strong>minimum</strong> number of elements to remove to make </em><code>nums<em>​​​</em></code><em> </em><em>a <strong>mountain array</strong>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The array itself is a mountain array so we do not need to remove any elements.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,1,1,5,6,2,3,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One solution is to remove the elements at indices 0, 1, and 5, making the array nums = [1,5,6,3,1].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li>It is guaranteed that you can make a mountain array out of <code>nums</code>.</li>
</ul>

class Solution {
public:
    int dp[1001][1002][3];
    int d(vector<int>&nums,int i,int prev,int smaller){
        if(i>=nums.size()){
            if(smaller==2) return 0;
            return 1e9;
        }
        if(dp[i][prev+1][smaller]!=-1) return dp[i][prev+1][smaller];
        
        if(prev==-1) return dp[i][prev+1][smaller]=min(d(nums,i+1,i,smaller),1+d(nums,i+1,prev,smaller));


        if(smaller==0){
            int include=1e9;
            int exclude=1+d(nums,i+1,prev,smaller);
            int mountain_index=1e9;
            if(nums[prev]<nums[i]){
                include=d(nums,i+1,i,smaller);
                mountain_index=d(nums,i+1,i,1);
            }
            return dp[i][prev+1][smaller]=min(mountain_index,min(include,exclude));
        }

        int include=1e9;
        int exclude=1+d(nums,i+1,prev,smaller);
        if(nums[prev]>nums[i])  include=d(nums,i+1,i,2);
        
        return dp[i][prev+1][smaller]=min(include,exclude);
    }
    int minimumMountainRemovals(vector<int>& nums) {
        memset(dp,-1,sizeof(dp));
        return d(nums,0,-1,0);
    }
};
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