<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 merge(int start,int mid,int end,vector<int>& arr){
    long long cnt=0;
    vector<int> temp(end - start + 1);
    int i=0;
    int left=start;
    int right=mid+1;
    while(left<=mid&&right<=end){
        if(arr[left]<=arr[right]){
            temp[i]=arr[left];
            i++;
            left++;
        }
        else{
            cnt+=mid-left+1;
            temp[i]=arr[right];
            i++;
            right++;

        }
    }
    while(left<=mid){
        temp[i]=arr[left];
            i++;
            left++;

    }
    while(right<=end){
        temp[i]=arr[right];
            i++;
            right++;

    }
    for(int k=start;k<=end;k++){
        arr[k]=temp[k-start];
    }
    
    return cnt;

}
long long merge_sort(int start,int end,vector<int>& arr){
 long long cnt=0;
    if(start<end){
        int mid=start+(end-start)/2;
        cnt+=merge_sort(start,mid,arr);
        cnt+=merge_sort(mid+1,end,arr);
        cnt+=merge(start,mid,end,arr);
    }
    return cnt;

}
    long long inversionCount(vector<int>& nums, int n) {
        vector<int> copy = nums; 
        return merge_sort(0,n-1,copy);
        
    }

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

        }
        return (global==local);
    }
};
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