<p>A car travels from a starting position to a destination which is <code>target</code> miles east of the starting position.</p>

<p>There are gas stations along the way. The gas stations are represented as an array <code>stations</code> where <code>stations[i] = [position<sub>i</sub>, fuel<sub>i</sub>]</code> indicates that the <code>i<sup>th</sup></code> gas station is <code>position<sub>i</sub></code> miles east of the starting position and has <code>fuel<sub>i</sub></code> liters of gas.</p>

<p>The car starts with an infinite tank of gas, which initially has <code>startFuel</code> liters of fuel in it. It uses one liter of gas per one mile that it drives. When the car reaches a gas station, it may stop and refuel, transferring all the gas from the station into the car.</p>

<p>Return <em>the minimum number of refueling stops the car must make in order to reach its destination</em>. If it cannot reach the destination, return <code>-1</code>.</p>

<p>Note that if the car reaches a gas station with <code>0</code> fuel left, the car can still refuel there. If the car reaches the destination with <code>0</code> fuel left, it is still considered to have arrived.</p>

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

<pre>
<strong>Input:</strong> target = 1, startFuel = 1, stations = []
<strong>Output:</strong> 0
<strong>Explanation:</strong> We can reach the target without refueling.
</pre>

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

<pre>
<strong>Input:</strong> target = 100, startFuel = 1, stations = [[10,100]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> We can not reach the target (or even the first gas station).
</pre>

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

<pre>
<strong>Input:</strong> target = 100, startFuel = 10, stations = [[10,60],[20,30],[30,30],[60,40]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We start with 10 liters of fuel.
We drive to position 10, expending 10 liters of fuel.  We refuel from 0 liters to 60 liters of gas.
Then, we drive from position 10 to position 60 (expending 50 liters of fuel),
and refuel from 10 liters to 50 liters of gas.  We then drive to and reach the target.
We made 2 refueling stops along the way, so we return 2.
</pre>

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

<ul>
	<li><code>1 &lt;= target, startFuel &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= stations.length &lt;= 500</code></li>
	<li><code>1 &lt;= position<sub>i</sub> &lt; position<sub>i+1</sub> &lt; target</code></li>
	<li><code>1 &lt;= fuel<sub>i</sub> &lt; 10<sup>9</sup></code></li>
</ul>

import heapq

class Solution:
    def minRefuelStops(self, target: int, startFuel: int, stations: List[List[int]]) -> int:
        # Max heap to store the fuel from the gas stations we've passed
        max_heap = []
        # Track the current amount of fuel and refueling stops
        fuel = startFuel
        stops = 0
        prev_position = 0
        
        # Go through each station and simulate driving to that point
        for position, station_fuel in stations:
            # Calculate the distance to the next station
            fuel -= position - prev_position
            prev_position = position
            
            # While fuel is not enough to get to the current station, refuel
            while fuel < 0 and max_heap:
                fuel += -heapq.heappop(max_heap)
                stops += 1
            
            # If still can't reach the station, return -1
            if fuel < 0:
                return -1
            
            # Add the fuel of the current station to the heap (negative to simulate max heap)
            heapq.heappush(max_heap, -station_fuel)
        
        # Finally, we need to drive from the last station to the target
        fuel -= target - prev_position
        
        # Refuel if necessary to reach the target
        while fuel < 0 and max_heap:
            fuel += -heapq.heappop(max_heap)
            stops += 1
        
        # If still not enough fuel to reach the target, return -1
        if fuel < 0:
            return -1
        
        return stops
    
16900