<p>You want to build some obstacle courses. You are given a <strong>0-indexed</strong> integer array <code>obstacles</code> of length <code>n</code>, where <code>obstacles[i]</code> describes the height of the <code>i<sup>th</sup></code> obstacle.</p>

<p>For every index <code>i</code> between <code>0</code> and <code>n - 1</code> (<strong>inclusive</strong>), find the length of the <strong>longest obstacle course</strong> in <code>obstacles</code> such that:</p>

<ul>
	<li>You choose any number of obstacles between <code>0</code> and <code>i</code> <strong>inclusive</strong>.</li>
	<li>You must include the <code>i<sup>th</sup></code> obstacle in the course.</li>
	<li>You must put the chosen obstacles in the <strong>same order</strong> as they appear in <code>obstacles</code>.</li>
	<li>Every obstacle (except the first) is <strong>taller</strong> than or the <strong>same height</strong> as the obstacle immediately before it.</li>
</ul>

<p>Return <em>an array</em> <code>ans</code> <em>of length</em> <code>n</code>, <em>where</em> <code>ans[i]</code> <em>is the length of the <strong>longest obstacle course</strong> for index</em> <code>i</code><em> as described above</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> obstacles = [1,2,3,2]
<strong>Output:</strong> [1,2,3,3]
<strong>Explanation:</strong> The longest valid obstacle course at each position is:
- i = 0: [<u>1</u>], [1] has length 1.
- i = 1: [<u>1</u>,<u>2</u>], [1,2] has length 2.
- i = 2: [<u>1</u>,<u>2</u>,<u>3</u>], [1,2,3] has length 3.
- i = 3: [<u>1</u>,<u>2</u>,3,<u>2</u>], [1,2,2] has length 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> obstacles = [2,2,1]
<strong>Output:</strong> [1,2,1]
<strong>Explanation: </strong>The longest valid obstacle course at each position is:
- i = 0: [<u>2</u>], [2] has length 1.
- i = 1: [<u>2</u>,<u>2</u>], [2,2] has length 2.
- i = 2: [2,2,<u>1</u>], [1] has length 1.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> obstacles = [3,1,5,6,4,2]
<strong>Output:</strong> [1,1,2,3,2,2]
<strong>Explanation:</strong> The longest valid obstacle course at each position is:
- i = 0: [<u>3</u>], [3] has length 1.
- i = 1: [3,<u>1</u>], [1] has length 1.
- i = 2: [<u>3</u>,1,<u>5</u>], [3,5] has length 2. [1,5] is also valid.
- i = 3: [<u>3</u>,1,<u>5</u>,<u>6</u>], [3,5,6] has length 3. [1,5,6] is also valid.
- i = 4: [<u>3</u>,1,5,6,<u>4</u>], [3,4] has length 2. [1,4] is also valid.
- i = 5: [3,<u>1</u>,5,6,4,<u>2</u>], [1,2] has length 2.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == obstacles.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= obstacles[i] &lt;= 10<sup>7</sup></code></li>
</ul>

class segTree{
    public: 
        vector<int> seg;
    segTree(int n){
        seg.resize(4*n,0);
    }
    void build(int idx, int left, int right, vector<int>& v){
        if(left==right){
            seg[idx] = v[left];
            return;
        }
        int mid = left + (right-left)/2;
        build(2*idx+1,left,mid,v);
        build(2*idx+2,mid+1,right,v);
        seg[idx] = max(seg[2*idx+1],seg[2*idx+2]);
    }
    void update(int idx, int left, int right, int pos, int val){
        if(left == right){
            seg[idx] = max(seg[idx],val);
            return;
        }
        int mid = left + (right-left)/2;
        if(mid >= pos) update(2*idx+1,left,mid,pos,val);
        else update(2*idx+2,mid+1,right,pos,val);
        seg[idx] = max(seg[2*idx+1],seg[2*idx+2]);
    }
    int query(int idx, int left, int right,int l, int r){
        
        if(left > r || right < l) return 0;

        if(left >= l && right <= r) return seg[idx];

        int mid = left + (right-left)/2;

        int lv = query(2*idx+1,left,mid,l,r);
        int rv = query(2*idx+2,mid+1,right,l,r);
        return max(lv,rv);
    }
};
class Solution {
public:
    void resizE(vector<int>& v){
        map<int,int> mp;
        for(auto &i : v) mp[i];
        int c = 0;
        for(auto &it : mp) it.second = c++;
        for(auto &i : v) i = mp[i];
    }
    vector<int> longestObstacleCourseAtEachPosition(vector<int>& v) {
        resizE(v);
        int m = *max_element(v.begin(),v.end()),n=v.size();
        segTree st(m+9);
        vector<int> res(n,0);
        // for(auto it : v) cout << it << " ";cout << endl;
        for(int i=0;i<n;i++){
            // query [0,v[i]]
            res[i] = st.query(0,0,m+8,0,v[i]) + 1;
            // update(v[i],res[i])
            st.update(0,0,m+8,v[i],res[i]);
        }
        return res;
    }
};
160000