<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>

#define ll long long
class Solution {
public:
    void update(int low, int high, int ind, int to_up, vector<ll> &seg){
        if(low == high){
            // if(to_up != low) return;
            seg[ind]++;
            return;
        }
        int mid = (low + high) / 2;
        if(to_up >= low && to_up <= mid) update(low, mid, 2*ind+1, to_up, seg);
        else update(mid+1, high, 2*ind+2, to_up, seg);
        seg[ind] = seg[2*ind+1] + seg[2*ind+2];
    }
    int query(int low, int high, int ind, int l, int r, vector<ll> &seg){
        if(low > r || high < l) return 0;
        if(low >= l && high <= r) return seg[ind];
        int mid = (low + high) / 2;
        int a = query(low, mid, 2*ind+1, l, r, seg);
        int b = query(mid+1, high, 2*ind+2, l, r, seg);
        return a+b;
    }
    bool isIdealPermutation(vector<int>& nums) {
        int n = nums.size();
        ll local = 0;
        for(int i = 0 ; i < n-1 ; i++){
            if(nums[i] > nums[i+1]) local++;
        }
        vector<ll> seg(4*(n+1)+4);
        ll global = 0;
        for(int i = 0 ; i < n ; i++){
            ll curr = query(0, n-1 ,0, nums[i]+1, n, seg);
            global += curr;
            update(0, n-1, 0, nums[i], seg);
        }
        // cout<<local<<' '<<global<<endl;
        return local == global;
    }
};
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