import heapq


class Solution:
    def lastStoneWeight(self, stones: list[int]) -> int:
        stones.append(0)
        stones = list(map(lambda x: -x, stones))
        heapq.heapify(stones)
        while len(stones) > 1:
            y, x = -heapq.heappop(stones), -heapq.heappop(stones)
            if x != y:
                heapq.heappush(stones, -(y - x))
        return -heapq.heappop(stones)

class Solution1:
    def backspaceCompare(self, s: str, t: str) -> bool:
        ss, st = [], []
        for c in s:
            if c != '#':
                ss.append(c)
            elif ss:
                ss.pop()
        for c in t:
            if c != '#':
                st.append(c)
            elif st:
                st.pop()
        return ss == st


class Solution:
    def backspaceCompare(self, s: str, t: str) -> bool:
        ps, pt = len(s) - 1, len(t) - 1  # pointer
        bs, bt = 0, 0  # backspace

        def go_left(string, pointer, backspace):
            while pointer >= 0 and (backspace or string[pointer] == '#'):
                backspace += (-1) ** (string[pointer] != '#')
                pointer -= 1
            return pointer, backspace

        while True:
            (ps, bs), (pt, bt) = go_left(s, ps, bs), go_left(t, pt, bt)
            if not (ps >= 0 and pt >= 0 and s[ps] == t[pt]):
                return ps == pt == -1
            ps -= 1
            pt -= 1

from collections import Counter


class Solution:
    def getHint(self, s: str, g: str) -> str:
        a, b = 0, 0
        cs, cg = Counter(), Counter()
        for i in range(len(s)):
            if s[i] == g[i]:
                a += 1
                continue
            if cg[s[i]]:
                cg[s[i]] -= 1
                b += 1
            else:
                cs[s[i]] += 1
            if cs[g[i]]:
                cs[g[i]] -= 1
                b += 1
            else:
                cg[g[i]] += 1
        return f'{a}A{b}B'

import math


class Solution1:
    def uniquePaths(self, m: int, n: int) -> int:
        return math.comb((m - 1) + (n - 1), (n - 1))


class Solution:
    def uniquePaths(self, m: int, n: int) -> int:
        dp = [1] + [0 for _ in range(n - 1)]
        for _ in range(m):
            for i in range(n - 1):
                dp[i + 1] += dp[i]
        return dp[n - 1]

class Solution:
    # https://leetcode.com/problems/longest-repeating-character-replacement/solutions/278271
    def characterReplacement(self, s: str, k: int) -> int:
        c, mf = {}, 0  # counter, max_freq
        l, N = 0, len(s)
        for r in range(N):
            c[s[r]] = c.get(s[r], 0) + 1
            mf = max(mf, c[s[r]])
            if not ((r + 1) - l - mf <= k):  # shift right
                c[s[l]] -= 1
                l += 1
            # find next if same
        return N - l  # length


class Solution2:
    # https://leetcode.com/problems/longest-repeating-character-replacement/solutions/278271
    def characterReplacement(self, s: str, k: int) -> int:
        result = 0
        c, mf = {}, 0  # counter, max_freq
        for r in range(len(s)):
            c[s[r]] = c.get(s[r], 0) + 1
            mf = max(mf, c[s[r]])
            if result - mf >= k:
                c[s[r - result]] -= 1
            else:
                result += 1  # update when more
        return result


class SolutionBS:  # TODO: review
    # https://leetcode.com/problems/longest-repeating-character-replacement/solutions/2805777
    def characterReplacement(self, s: str, k: int) -> int:
        def too_long(length: int):
            c, mf = {}, 0
            l = 0
            for r in range(len(s)):
                c[s[r]] = c.get(s[r], 0) + 1
                if r + 1 - l > length:
                    c[s[l]] -= 1
                    l += 1
                mf = max(mf, c[s[r]])
                if length - mf <= k:
                    return False
            return True

        l, r = 0, len(s)
        while l < r:
            m = (l + r) // 2
            length = m + 1
            l, r = (l, m) if too_long(length) else (m + 1, r)
        return (l - 1) + 1

from collections import Counter


class Solution:
    def findAnagrams(self, s: str, p: str) -> list[int]:
        result, s, P = [], s + ' ', len(p)
        cp, cs = Counter(p), Counter(s[:P])
        for i in range(len(s) - P):
            if cp == cs:
                result.append(i)
            cs.subtract(s[i])
            cs.update(s[i + P])
        return result

class Solution:
    def climbStairs(self, n: int) -> int:
        a, b = 1, 1
        for _ in range(n):
            a, b = b, a + b
        return a

class Solution:
    def fib(self, n: int) -> int:
        a, b = 0, 1
        for _ in range(n):
            a, b = b, a + b
        return a

class Solution:
    def minCostClimbingStairs(self, cost: list[int]) -> int:
        a = b = 0
        for c in cost:
            a, b = b, min(a, b) + c
        return min(a, b)

class Solution:
    def computeArea(
        self,
        ax1: int,
        ay1: int,
        ax2: int,
        ay2: int,
        bx1: int,
        by1: int,
        bx2: int,
        by2: int,
    ) -> int:
        (ax1, ax2), (ay1, ay2), (bx1, bx2), (by1, by2) = map(
            sorted,
            ((ax1, ax2), (ay1, ay2), (bx1, bx2), (by1, by2)),
        )
        return sum(
            (
                (ax2 - ax1) * (ay2 - ay1),
                (bx2 - bx1) * (by2 - by1),
                -(
                    max(0, min(ax2, bx2) - max(ax1, bx1))
                    * max(0, min(ay2, by2) - max(ay1, by1))
                ),
            )
        )

# The guess API is already defined for you.
# @param num, your guess
# @return -1 if num is higher than the picked number
#          1 if num is lower than the picked number
#          otherwise return 0
def guess(num: int) -> int:
    ...


class Solution:
    def guessNumber(self, n: int) -> int:
        l, r = 0, n
        while l < r:
            m = (l + r) // 2
            if not guess(m):
                return m
            l, r = (l, m) if guess(m) < 0 else (m + 1, r)
        return l

class Solution:
    def numIslands(self, grid) -> int:
        M, N = len(grid), len(grid[0])

        def dfs(m, n):
            r = 0 <= m < M and 0 <= n < N and grid[m][n] == '1'
            if r:
                grid[m][n] = None
                list(map(dfs, (m + 1, m - 1, m, m), (n, n, n + 1, n - 1)))
            return r

        return sum(dfs(m, n) for m in range(M) for n in range(N))

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None


class Solution:
    def lowestCommonAncestor(self, root, p, q):
        if root.val > max(p.val, q.val):
            return self.lowestCommonAncestor(root.left, p, q)
        if root.val < min(p.val, q.val):
            return self.lowestCommonAncestor(root.right, p, q)
        return root

class Solution:
    def floodFill(
        self, image: list[list[int]], sr: int, sc: int, color: int
    ) -> list[list[int]]:
        COLOR, M, N = image[sr][sc], len(image), len(image[0])

        def dfs(m, n):
            if not all([0 <= m < M, 0 <= n < N]):
                return

            if not all([image[m][n] == COLOR, image[m][n] != color]):
                return

            image[m][n] = color
            list(map(dfs, (m + 1, m - 1, m, m), (n, n, n + 1, n - 1)))

        dfs(sr, sc)
        return image

class Solution1:
    def removeDuplicates(self, nums: list[int]) -> int:
        v, p = -101, 0  # ng
        for i in range(len(nums)):
            if nums[i] > v:
                v = nums[p] = nums[i]
                p += 1
        return p


class Solution:
    def removeDuplicates(self, nums: list[int]) -> int:
        p = 1
        for i in range(1, len(nums)):
            if nums[p - 1] < nums[i]:
                nums[p], p = nums[i], p + 1
        return p

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def isValidBST(self, root, lo=float('-inf'), hi=float('inf')) -> bool:
        '''
        [5,4,6,null,null,3,7] => false
        '''
        return (not root) or all(
            [
                lo < root.val < hi,
                self.isValidBST(root.left, lo, root.val),
                self.isValidBST(root.right, root.val, hi),
            ]
        )

from functools import reduce


# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def levelOrder(self, root) -> list[list[int]]:
        result, q = [], [root]
        while True:
            q = [x for x in q if x]
            v = [x.val for x in q]
            if not v:
                break
            result.append(v)
            q = reduce(lambda a, b: a + [b.left, b.right], q, [])
        return result

class Solution:
    def search(self, nums: list[int], target: int) -> int:
        l, r = 0, len(nums)
        while l < r:
            m = (l + r) // 2
            if nums[m] == target:
                return m
            l, r = (l, m) if nums[m] > target else (m + 1, r)
        return -1

class Solution:
    def maxProfit(self, prices) -> int:
        l, r = prices[0], 0
        for p in prices:
            l, r = min(l, p), max(r, p - l)
        return r

class Solution:
    def detectCycle(self, head):
        '''
        .___a___.___C-b___.
                (_________) -> C: cycle
                     b

        slow: a+C-b + xC
        fast: a+C-b + yC

        2 slow = fast
        => a+C-b = (y-2x)C
        => a = (y-2x-1)C+b

        .___(y-2x-1)C+b___.___C-b___.
                          (_________)
                               b

        => a mod C = b mod C
        '''
        l = r = head
        while r and r.next:
            l, r = l.next, r.next.next
            if l is r:
                break
        else:
            return

        while head is not r:
            head, r = head.next, r.next
        return head

class Solution:
    def longestPalindrome(self, s: str) -> int:
        r, pool = 0, set()
        for c in s:
            if c in pool:
                pool.remove(c)
                r += 1
            else:
                pool.add(c)
        return r * 2 + bool(pool)

"""
# Definition for a Node.
class Node:
    def __init__(self, val=None, children=None):
        self.val = val
        self.children = children
"""


class Solution:
    def preorder(self, root):
        return (
            (root.val,) + sum((self.preorder(x) for x in root.children), ())
            if root
            else ()
        )