<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>

int dp[1002][1002][2][2];

class Solution {
private:
    vector <int> arr;
    int fun(int ind, int prev, int mustDec,int mustInc)
    {
        if(ind>=arr.size())
        {
            if(mustDec)return 0;
            return -1e6;
        }
        if(dp[ind][prev][mustDec][mustInc]!=-1)
            return dp[ind][prev][mustDec][mustInc];
        int noPick = fun(ind+1,prev,mustDec,mustInc);
        int pick = -1e6;
        if(mustInc && arr[ind] > arr[prev])
            pick = fun(ind+1,ind,0,0) + 1;
        if(mustDec && arr[ind] < arr[prev])
            pick = fun(ind+1,ind,1,0) + 1;
        if(!mustDec && !mustInc)
        {
            if(arr[ind] > arr[prev])
                pick = max(pick,fun(ind+1,ind,0,0) + 1);
            if(arr[ind] < arr[prev])
                pick = max(pick,fun(ind+1,ind,1,0) + 1);
        }
        return dp[ind][prev][mustDec][mustInc] = max(pick,noPick);
    }
public:
    int minimumMountainRemovals(vector<int>& nums) {
        arr = nums;
        int ans = 0;
        int n = nums.size();
        memset(dp,-1,sizeof(dp));
        for(int i = 0; i < n; i++)
            ans = max(ans,fun(i+1,i,0,1) + 1);
        return n - ans;
    }
};
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