<p>A robot on an infinite XY-plane starts at point <code>(0, 0)</code> facing north. The robot receives an array of integers <code>commands</code>, which represents a sequence of moves that it needs to execute. There are only three possible types of instructions the robot can receive:</p>

<ul>
	<li><code>-2</code>: Turn left <code>90</code> degrees.</li>
	<li><code>-1</code>: Turn right <code>90</code> degrees.</li>
	<li><code>1 &lt;= k &lt;= 9</code>: Move forward <code>k</code> units, one unit at a time.</li>
</ul>

<p>Some of the grid squares are <code>obstacles</code>. The <code>i<sup>th</sup></code> obstacle is at grid point <code>obstacles[i] = (x<sub>i</sub>, y<sub>i</sub>)</code>. If the robot runs into an obstacle, it will stay in its current location (on the block adjacent to the obstacle) and move onto the next command.</p>

<p>Return the <strong>maximum squared Euclidean distance</strong> that the robot reaches at any point in its path (i.e. if the distance is <code>5</code>, return <code>25</code>).</p>

<p><strong>Note:</strong></p>

<ul>
	<li>There can be an obstacle at <code>(0, 0)</code>. If this happens, the robot will ignore the obstacle until it has moved off the origin. However, it will be unable to return to <code>(0, 0)</code> due to the obstacle.</li>
	<li>North means +Y direction.</li>
	<li>East means +X direction.</li>
	<li>South means -Y direction.</li>
	<li>West means -X direction.</li>
</ul>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,3], obstacles = []</span></p>

<p><strong>Output:</strong> <span class="example-io">25</span></p>

<p><strong>Explanation: </strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 4 units to <code>(0, 4)</code>.</li>
	<li>Turn right.</li>
	<li>Move east 3 units to <code>(3, 4)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(3, 4)</code>, which squared is <code>3<sup>2</sup> + 4<sup>2 </sup>= 25</code> units away.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,4,-2,4], obstacles = [[2,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">65</span></p>

<p><strong>Explanation:</strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 4 units to <code>(0, 4)</code>.</li>
	<li>Turn right.</li>
	<li>Move east 1 unit and get blocked by the obstacle at <code>(2, 4)</code>, robot is at <code>(1, 4)</code>.</li>
	<li>Turn left.</li>
	<li>Move north 4 units to <code>(1, 8)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(1, 8)</code>, which squared is <code>1<sup>2</sup> + 8<sup>2</sup> = 65</code> units away.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [6,-1,-1,6], obstacles = [[0,0]]</span></p>

<p><strong>Output:</strong> <span class="example-io">36</span></p>

<p><strong>Explanation:</strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 6 units to <code>(0, 6)</code>.</li>
	<li>Turn right.</li>
	<li>Turn right.</li>
	<li>Move south 5 units and get blocked by the obstacle at <code>(0,0)</code>, robot is at <code>(0, 1)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(0, 6)</code>, which squared is <code>6<sup>2</sup> = 36</code> units away.</p>
</div>

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

<ul>
	<li><code>1 &lt;= commands.length &lt;= 10<sup>4</sup></code></li>
	<li><code>commands[i]</code> is either <code>-2</code>, <code>-1</code>, or an integer in the range <code>[1, 9]</code>.</li>
	<li><code>0 &lt;= obstacles.length &lt;= 10<sup>4</sup></code></li>
	<li><code>-3 * 10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 3 * 10<sup>4</sup></code></li>
	<li>The answer is guaranteed to be less than <code>2<sup>31</sup></code>.</li>
</ul>

class Solution {
public:
    int upperBound(int s , int e , int target , vector<int>& v){
        if(s <= e){
            int m = s + (e-s)/2;
            if(v[m] >= target && (m == 0 || v[m-1] < target)){
                return v[m];
            }
            return ((v[m] < target) ? upperBound(m+1,e,target,v) : upperBound(s,m-1,target,v));
        }
        return 0;
    }
    int lowerBound(int s , int e , int target , vector<int>& v){
        if(s <= e){
            int m = s + (e-s)/2;
            if(v[m] <= target && (m == v.size()-1 || v[m+1] > target)){
                return v[m];
            }
            return ((v[m] < target) ? lowerBound(m+1,e,target,v) : lowerBound(s,m-1,target,v));
        }
        return 0;
    }
    int robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        map<int,vector<int>> xc,yc;
        for(auto x:obstacles){
            xc[x[0]].push_back(x[1]);
            yc[x[1]].push_back(x[0]);
        }
        for(auto x:xc){
            sort(xc[x.first].begin(),xc[x.first].end());
        }
        for(auto x:yc){
            sort(yc[x.first].begin(),yc[x.first].end());
        }

        // for(auto x:yc[0]){
        //     cout << x << " ";
        // }
        // cout<<"\n---\n";

        int ans = 0;
        int dir = 1;
        int X = 0;
        int Y = 0;
        for(auto x:commands){
            if(x == -1){
                dir = ((dir == 4) ? 1 : dir+1);
            }
            else if(x == -2){
                dir = ((dir == 1) ? 4 : dir-1);
            }
            else{
                if(dir == 1){
                    if(xc[X].empty() || xc[X].back() <= Y){
                        Y += x;
                    }
                    else{
                        int upper = upperBound(0,xc[X].size()-1,Y+1,xc[X]);
                        Y = min(Y+x,upper-1);
                    }
                }
                else if(dir == 2){
                    if(yc[Y].empty() || yc[Y].back() <= X){
                        X += x;
                    }
                    else{
                        int upper = upperBound(0,yc[Y].size()-1,X+1,yc[Y]);
                        X = min(X+x,upper-1);
                    }
                }
                else if(dir == 3){
                    if(xc[X].empty() || xc[X][0] >= Y){
                        Y -= x;
                    }
                    else{
                        int lower = lowerBound(0,xc[X].size()-1,Y-1,xc[X]);
                        Y = max(Y-x,lower+1);
                    }
                }
                else{
                    if(yc[Y].empty() || yc[Y][0] >= X){
                        X -= x;
                    }
                    else{
                        int lower = lowerBound(0,yc[Y].size()-1,X-1,yc[Y]);
                        X = max(X-x,lower+1);
                    }
                }
                // cout << X << " " << Y << endl;
                ans = max(ans,X*X+Y*Y);
            }
        }

        return ans;
    }
};
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