<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 int gcnt=0;
    void merge(vector<int>& nums, int low, int mid, int high){
        int left=low,right=mid+1,n=high-low+1,k=0;
        vector<int>temp(n,0);
        while(left<=mid&&right<=high){
            if(nums[left]<=nums[right]){
                temp[k++]=nums[left++];
                
            } else{
                gcnt+=(mid-left+1);
                temp[k++]=nums[right++];
            }
        }
        while(left<=mid){
            temp[k++]=nums[left++];
        }
        while(right<=high){
            temp[k++]=nums[right++];
        }
        for(int i=0;i<n;i++){
            nums[i+low]=temp[i];
        }
    }
    void mergeSort(vector<int>& nums, int low,int high){
        if(low<high){
            int mid=low+(high-low)/2;
            mergeSort(nums,low,mid);
            mergeSort(nums,mid+1,high);
            merge(nums,low,mid,high);
        }
    }
    bool isIdealPermutation(vector<int>& nums) {
        int lcnt=0,n=nums.size();
        for(int i=0;i<n-1;i++){
            if(nums[i]>nums[i+1])
            lcnt++;
        }
        gcnt=0;
        mergeSort(nums,0,n-1);
        cout<<lcnt<<" "<<gcnt<<endl;
        return lcnt==gcnt;
    }
};
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