<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][1001][3];
    int solve(int i,int j,int k,vector<int>&nums){
        if(i==nums.size()){
        if(k!=2)
        return 1000;
        else
        return 0;
        }
        if(dp[i][j][k]!=-1)
        return dp[i][j][k];

        if(!k){
            if(i==j){
                return dp[i][j][k] = min(1+solve(i+1,i+1,k,nums),solve(i+1,j,k,nums));
            }
            else {
                int ans = solve(i+1,j,k,nums)+1;
                if(nums[i]>nums[j]){
                    ans = min(ans,solve(i+1,i,0,nums));
                    ans = min(ans,solve(i+1,i,1,nums));
                }
                // cout<<i<<" "<<j<<" "<<k<<" "<<ans<<endl;
                return dp[i][j][k] = ans;
            }
        }
        else if(k==1){
            int ans = solve(i+1,j,k,nums)+1;
            if(nums[i]<nums[j]){
                ans = min(ans,solve(i+1,i,2,nums));
            }
            // cout<<i<<" "<<j<<" "<<k<<" "<<ans<<endl;
            return dp[i][j][k] = ans;
        }
        else{
            int ans = solve(i+1,j,k,nums)+1;
            if(nums[i]<nums[j]){
                ans = min(ans,solve(i+1,i,k,nums));
            }
            // cout<<i<<" "<<j<<" "<<k<<" "<<ans<<endl;
            return dp[i][j][k] = ans;
        }
    }
    int minimumMountainRemovals(vector<int>& nums) {
        memset(dp,-1,sizeof(dp));
        return solve(0,0,0,nums);
    }
};
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