<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 BIT{
public:
    vector<long long> v;
    BIT(long long n){
        v = vector<long long>(n+10,0);
    };

    void up(long long ix,long long vul)
    {
        for(ix++; ix<(long long)v.size(); ix+=(ix&-ix))
            v[ix]=(v[ix]+vul);
    }

    long long presum(long long ix)
    {
        long long ans =  0;
        for(ix++; ix>0; ix-=(ix&-ix))
            ans=(ans+v[ix]);
        return ans;
    }

};

class Solution {
public:
    bool isIdealPermutation(vector<int>& v) {
        
        BIT b(v.size());
        int ans  = 0;
        for(int i=0; i<v.size(); ++i){
            ans+=(i-b.presum(v[i]));
            // cout<<ans<<" ";
            b.up(v[i],1);
        }
        
        // cout<<ans<<" ";
        for(int i=0; i+1<v.size(); ++i){
            ans-=(v[i]>v[i+1]);
        }
    
        // cout<<ans<<endl;;
        return !ans;
        
        
    }
};
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