<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 i,int j,int mid,vector<int>&nums,int x)
    {
        int left=i,right=mid+1,n=j-i+1;
        vector<int>temp(n,0);
        long long k=0,ans=0;
        while(left<=mid and right<=j)
        {
            if(nums[left]>nums[right])
            {
                ans+=(mid-left+1);
                temp[k++]=nums[right++];
            }
            else
            {
                temp[k++]=nums[left++];
            }
        }
        while(left<=mid)
        {
            temp[k++]=nums[left++];
        }
        while(right<=j)
        {
            temp[k++]=nums[right++];
        }
        k=0;
        for(int p=i;p<=j;p++)
        {
            nums[p]=temp[k++];
        }
        return ans;
    }
    long long f(int i,int j,vector<int>&nums,int &x)
    {
        long long ans=0;
        if(i<j) 
        {int mid=(i+j)/2;
        ans+=f(i,mid,nums,x);
        ans+=f(mid+1,j,nums,x);
        ans+=merge(i,j,mid,nums,x);}
        return ans;
    }
    bool isIdealPermutation(vector<int>& nums) {
        long long cnt=0;
        int x=0;
         for(int i=0;i<nums.size()-1;i++)
        {
            if(nums[i]>nums[i+1]) cnt++;
        }
        long long ans=f(0,nums.size()-1,nums,x);
        cout<<ans<<endl;
       
        cout<<cnt<<endl;
        if(cnt!=ans) return false;
        return true;
    }
};
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