<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:
    vector<int>temp;

int merge2(int st,int md,int end,vector<int>& nums){
   int c=0;
   for (int i = st,j=md+1,k = st; k <= end; k++){
        if(i>md)
          temp[k]=nums[j++];
        else if(j>end)
          temp[k]=nums[i++];
        else if(nums[i]<nums[j])
          temp[k]=nums[i++];
        else{
          temp[k]=nums[j++];
          c+=md-i+1; 
        }       
   }
   for (int i = st; i <= end; i++)
		nums[i] = temp[i];

    return c;
}


long long merge_sort(int st,int end,vector<int>& nums){
    if(st==end)return 0;
  int md=(st+end)/2;
  long long res = merge_sort(st,md,nums); 
  res += merge_sort(md+1,end,nums);
  
  res+=merge2(st,md,end,nums);

  return res; 
}


bool isIdealPermutation(vector<int>& nums) {
    int local=0;
    temp.resize(nums.size());
    for (int i = 1; i < nums.size(); i++)
        if(nums[i-1] > nums[i])local++;
    
    long long global=merge_sort(0,nums.size()-1,nums);
    return local==global;
        
}



};
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