<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:
    bool isIdealPermutation(vector<int>& nums) {
        int n = nums.size();
        int localInversions = 0;
        for(int i = 0; i<n-1; i++) {
            if(nums[i]>nums[i+1])localInversions++;
        }
        int globalInversions = mergeCount(0, n-1, nums);
        return localInversions==globalInversions;
    }
private:
    long long mergeCount(int st, int end, vector<int>& nums) {
        if(st>=end)return 0;
        long long cnt = 0;
        int mid = st + (end - st)/2;
        cnt += mergeCount(st, mid, nums);
        cnt += mergeCount(mid + 1, end, nums);
        cnt += merge(st, end, mid, nums);
        return cnt;
    }
    long long merge(int st, int end, int mid, vector<int>& nums) {
        long long cnt = 0;
        int j = mid + 1;
        for(int i = st; i<=mid; i++) {
            while(j<=end && nums[i]>nums[j]) {
                j++;
            }
            cnt+= j - (mid + 1);
        }
        int sz = end - st + 1;
        vector<int> temp(sz, 0);
        int l = st, r = mid + 1, k = 0;
        while(l<=mid && r<=end) {
            if(nums[l]<nums[r]) {
                temp[k++] = nums[l++];
            } else {
                temp[k++] = nums[r++];
            }
        }
        while(l<=mid) {
            temp[k++] = nums[l++];
        }
        while(r<=end) {
            temp[k++] = nums[r++];
        }
        int m = 0;
        for(int i = st; i<=end; i++) {
            nums[i] = temp[m++];
        }
        return cnt;
    }
};
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