<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 {
    void merge(int l,int m, int h, vector<int>& nums, long long &globalCnt){
        vector<int> tmp(h-l+1);
        int i=l,j=m+1,k=0;

        while(i<=m && j<=h){
            if(nums[i]<=nums[j]){
                tmp[k++]=nums[i++];
            }
            else{
                globalCnt+=m-i+1;
                tmp[k++]=nums[j++];
            }
        }

        while(i<=m){
            tmp[k++]=nums[i++];
        }

        while(j<=h){
            tmp[k++]=nums[j++];
        }

        for(int i=0;i<k;i++){
            nums[l+i]=tmp[i];
        }
        return;
    }
    void mergeSort(int l, int h, vector<int>& nums,long long &globalCnt){
        if(l>=h) return;
        int m=l+(h-l)/2;
        mergeSort(l,m,nums,globalCnt);
        mergeSort(m+1,h,nums,globalCnt);
        merge(l,m,h,nums,globalCnt);
        return;
    }
    long long globalInversions(vector<int> nums){
        long long cnt=0;
        mergeSort(0,nums.size()-1,nums,cnt);
        return cnt;
    }   
    long long localInversions(vector<int>& nums){
        long long cnt=0;
        for(int i=0;i<nums.size()-1;i++){
            if(nums[i]>nums[i+1]){
                cnt++;
            }
        }
        return cnt;
    }
public:
    bool isIdealPermutation(vector<int>& nums) {
        // cout<<"localInversions: "<<localInversions(nums)<<endl;
        // cout<<"globalInversions: "<<globalInversions(nums)<<endl;
        return globalInversions(nums)==localInversions(nums);
    }
};
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