<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 Compare{
    public: 
    bool operator()(pair<int,int>p1,pair<int,int>p2){
        return p1.second>p2.second;
    }
};
class Solution {
public:
    bool isIdealPermutation(vector<int>& nums) {
        int n=nums.size();
        if(n<=1){
            return true;
        }
        priority_queue<int>q;
        for(int i=0;i<n-1;i++){
            int curr=nums[i];
            int next=nums[i+1];
            if(!q.empty()){
                if(q.top()>next){
                    return false;
                }
            }
            q.push(curr);
        }
        return true;
    //     int gcount=0;
    //     int lcount=0;
    //     priority_queue<pair<int, int>, vector<pair<int, int>>, Compare>q;
    // //   for(int i=0;i<n;i++){
    // //     for(int j=i+1;j<n;j++){
    // //        if(nums[i]>nums[j]){
    // //         gcount++;
    // //        }
    // //     }
    // //   } 
    // q.push({0,nums[n-1]}); 
    // for(int i=n-2;i>=0;i--){
    //     int cnt=0;
    //     while(!q.empty() && q.top().second<nums[i]){
    //         if(q.top().first==0){
    //             cnt+=1;
    //         }
    //         else
    //      cnt+=q.top().first;
    //      q.pop();
    //     }       
    //   q.push({cnt,nums[i]});
    // }
    // while(!q.empty()){
    // gcount+=q.top().first;
    //   q.pop();
    // }

    //   for(int i=0;i<n-1;i++){
    //     if(nums[i]>nums[i+1]){
    //         lcount++;
    //     }
    //   }
    //   cout<<gcount<<endl;
    //   cout<<lcount<<endl;

    //   if(gcount==lcount){
    //     return true;
    //   }
    //   return false;
    }
};
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