<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(vector<int>& nums, int s, int mid, int e){
        int n = e - s + 1;
        vector<int> temp(n);
        int i = s, j = mid + 1, k = 0;
        long long  cnt = 0;
        while(i <= mid  && j <= e){
            if(nums[i] > nums[j]){
                cnt += mid - i + 1;
                temp[k++] = nums[j++];
            }
            else{
                temp[k++] = nums[i++];
            }
        }
        while(i <= mid){
            temp[k++] = nums[i++];
        }
        while(j <= e){
            temp[k++] = nums[j++];
        }
        for(int i = s; i <= e; i++){
            nums[i] = temp[i - s];
        }
        return cnt;
    }
    long long mergeSort(vector<int> & nums, int s, int e){
        long long cnt = 0;
        if(s >= e) return cnt;
        int mid = (s + e)/2;
        cnt += mergeSort(nums, s, mid);
        cnt += mergeSort(nums, mid + 1, e);
        cnt += merge(nums, s, mid, e);
        // cout<<cnt<<endl;
        return cnt;
    }
    bool isIdealPermutation(vector<int>& nums) {
        int n = nums.size(), loc = 0;
        for(int i = 0; i < n - 1; i++){
            if(nums[i] > nums[i + 1]) loc++;
        }
        long long glo = mergeSort(nums, 0 , n - 1);
        // for(int i = 0; i < nums.size(); i++) cout<<nums[i]<<" ";
        // cout<<loc<<" "<<glo;
        return (loc == glo);

        
    }
};
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