<p>A frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.</p>

<p>Given a list of <code>stones</code>&nbsp;positions (in units) in sorted <strong>ascending order</strong>, determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be <code>1</code> unit.</p>

<p>If the frog&#39;s last jump was <code>k</code> units, its next jump must be either <code>k - 1</code>, <code>k</code>, or <code>k + 1</code> units. The frog can only jump in the forward direction.</p>

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

<pre>
<strong>Input:</strong> stones = [0,1,3,5,6,8,12,17]
<strong>Output:</strong> true
<strong>Explanation:</strong> The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.
</pre>

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

<pre>
<strong>Input:</strong> stones = [0,1,2,3,4,8,9,11]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.
</pre>

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

<ul>
	<li><code>2 &lt;= stones.length &lt;= 2000</code></li>
	<li><code>0 &lt;= stones[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>stones[0] == 0</code></li>
	<li><code>stones</code>&nbsp;is sorted in a strictly increasing order.</li>
</ul>

class Solution:
    def canCross(self, stones: List[int]) -> bool:
        if stones[0] != 0 or stones[1] != 1:
            return False
        if len(stones) == 2:
            return True

        visited = set()
        can_jump = set(stones)
        target = stones[-1]

        stack = []

        stack.append(4097)
        mask = (1 << 12) - 1

        while stack:
            state = stack.pop()
            pos = state >> 12
            step = state & mask
            # print(f'state {pos} {step}')

            for i in range(-1, 2):
                next_step = step + i
                next_pos = pos + next_step
                # print(f'trying {next_pos} {step+i}')
                if next_step > 0 and next_pos in can_jump:
                    if next_pos == target:
                        return True
                    if next_pos > target:
                        continue
                    next_state = (next_pos << 12) + next_step
                    if next_state not in visited:
                        visited.add(next_state)
                        stack.append(next_state)
                        # print(f'appended {next_pos} {next_step}')
        return False
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