<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:
    char direction[4] = {'N', 'E', 'S', 'W'};
    set<int> cols[(int)2e5];
    set<int> rows[(int)2e5];
    int shift = (int)1e5;
    
    pair<int, int> move(int curX, int curY, char direction, int moves) {
        if(direction == 'N') {
            return {curX, curY + moves};
        } else if(direction == 'S') {
            return {curX, curY - moves};
        } else if(direction == 'E') {
            return {curX + moves, curY};
        } else {
            return {curX - moves, curY};
        }
    }

    long long calcAns(long long x, long long y) {
        x -= shift;
        y -= shift;
        return x * x + y * y;
    }

    long long robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        int idx = 0;
        int x = shift, y = shift;
        long long ans = 0;
        for(auto &ob: obstacles) {
            int xx = ob.front();
            int yy = ob.back();

            cols[yy + shift].insert(xx + shift);
            rows[xx + shift].insert(yy + shift);
        }

        for(auto &c: commands) {
            if(c == -1) {
                idx++;
                if(idx == 4)
                    idx = 0;
                continue;
            }
            if(c == -2) {
                idx--;
                if(idx < 0)
                    idx = 3;

                continue;
            }
            int nx, ny;
            tie(nx, ny) = move(x, y, direction[idx], c);

            if(nx != x) {
                // horizontal move (rows change)
                // x changes
                if(nx > x) {
                    int obs = INT_MAX;
                    if(cols[y].upper_bound(x) != cols[y].end())
                        obs = *cols[y].upper_bound(x);
                    
                    // cout << "X OBS " << obs - shift << endl;
                    nx = min(nx, obs - 1);
                } else {
                    int obs = INT_MIN;
                    if(cols[y].lower_bound(x) != cols[y].begin())
                        obs = *(--cols[y].lower_bound(x));
                    
                    nx = max(nx, obs + 1);
                }
                
            } else {
                // y changes
                if(ny > y) {
                    int obs = INT_MAX;
                    if(rows[x].upper_bound(y) != rows[x].end()) {
                        obs = *rows[x].upper_bound(y);
                    }
                        
                    // cout << "Y OBS " << obs - shift << endl;
                    ny = min(ny, obs - 1);
                } else {
                    int obs = INT_MIN;
                    if(rows[x].lower_bound(y) != rows[x].begin())
                        obs = *(--rows[x].lower_bound(y));
                    
                    ny = max(ny, obs + 1);
                }
            }
            x = nx, y = ny;
            ans = max(ans, calcAns(x, y));
            // cout << "move " << x - shift << " " << y - shift << endl;
        }

        return ans;
    }
};
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