<p>You are given an integer array <code>nums</code> of length <code>n</code> which represents a permutation of all the integers in the range <code>[0, n - 1]</code>.</p>

<p>The number of <strong>global inversions</strong> is the number of the different pairs <code>(i, j)</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; n</code></li>
	<li><code>nums[i] &gt; nums[j]</code></li>
</ul>

<p>The number of <strong>local inversions</strong> is the number of indices <code>i</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; n - 1</code></li>
	<li><code>nums[i] &gt; nums[i + 1]</code></li>
</ul>

<p>Return <code>true</code> <em>if the number of <strong>global inversions</strong> is equal to the number of <strong>local inversions</strong></em>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,0,2]
<strong>Output:</strong> true
<strong>Explanation:</strong> There is 1 global inversion and 1 local inversion.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,0]
<strong>Output:</strong> false
<strong>Explanation:</strong> There are 2 global inversions and 1 local inversion.
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt; n</code></li>
	<li>All the integers of <code>nums</code> are <strong>unique</strong>.</li>
	<li><code>nums</code> is a permutation of all the numbers in the range <code>[0, n - 1]</code>.</li>
</ul>

class Solution {
public:
    long long ans = 0;
     void count(vector<int> &nums,int l,int mid,int h)
    {
        int i=l,j=mid+1;
        while(i<=mid && j<=h)
        {
            if(nums[i]>nums[j])
            {
                ans+=mid-i+1;
                j++;
            }
            else
            {
                i++;
            }
        }
    }
     void mergeSort(vector<int> &nums,int l,int mid,int h)
     {
          vector<int> dp(h-l+1,0);

          int i=l,j=mid+1,k=0;
          count(nums,l,mid,h);
          while(i<=mid && j<=h)
          {
               if(nums[i]<nums[j])
               {
                    // if((2*nums[i])<nums[j])
                    // {
                    //      ans+=h-j+1;
                    // }
                    dp[k++] = nums[i++];
               }
               else
               {
                    dp[k++] = nums[j++];
               }
          }

          while(i<=mid)
          {
               dp[k++] = nums[i++];
          }
          while(j<=h)
          {
               dp[k++]= nums[j++];
          }
          for(int i=0;i<k;i++)
          {
               nums[i+l] = dp[i];
          }
     }
     void merge(vector<int> &nums,int l,int h)
     {
          if(l<h)
          {
               int mid = (l+h)/2;
               merge(nums,l,mid);
               merge(nums,mid+1,h);
               mergeSort(nums,l,mid,h);
          }
     }
    bool isIdealPermutation(vector<int>& nums) {
        int local =0;
        for(int i=0;i<nums.size()-1;i++)
        {
            if(nums[i]>nums[i+1])local++;
        }
        merge(nums,0,nums.size()-1);
        return local == ans;
    }
};
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