<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:
    vector<int> lis(vector<int>arr,int n)
    {
        vector<int>dp(n,1);
        for(int i=1;i<n;i++)
        {
            for(int j=0;j<i;j++)
            {
                if(arr[i]>arr[j])
                    dp[i]=max(dp[i],dp[j]+1);
            }
        }
        return dp;
    }
    vector<int> lds(vector<int>arr,int n)
    {
        vector<int>dp(n,1);
        for(int i=n-2;i>=0;i--)
        {
            for(int j=i+1;j<n;j++)
            {
                if(arr[i]>arr[j])
                    dp[i]=max(dp[i],dp[j]+1);
            }
        }
        return dp;
    }
    int minimumMountainRemovals(vector<int>& arr) {
        int n=arr.size();
        vector<int> left=lis(arr,n);
        vector<int> right=lds(arr,n);
        int res=0;
        for(int i=0;i<n;i++)
        {
            int curr;
            if(left[i]==1 || right[i]==1)
                curr=0;
            else
                curr=left[i]+right[i]-1;
            res=max(res,curr);
        }
        return n-res;
    }
};
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