import bisect import copy import decimal import fractions import heapq import itertools import math import random import sys import time from collections import Counter,deque,defaultdict from functools import lru_cache,reduce from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max def _heappush_max(heap,item): heap.append(item) heapq._siftdown_max(heap, 0, len(heap)-1) def _heappushpop_max(heap, item): if heap and item < heap[0]: item, heap[0] = heap[0], item heapq._siftup_max(heap, 0) return item from math import gcd as GCD read=sys.stdin.read readline=sys.stdin.readline readlines=sys.stdin.readlines write=sys.stdout.write #import pypyjit #pypyjit.set_param('max_unroll_recursion=-1') #sys.set_int_max_str_digits(10**9) def Cartesian_Tree(lst,maximize=False,leftright=False): N=len(lst) parents=[None]*N stack=[] for i in range(N): prev=None while stack and (not maximize and lst[i]lst[stack[-1]]): prev=stack.pop() if prev!=None: parents[prev]=i if stack: parents[i]=stack[-1] stack.append(i) root=-1 graph=[[] for x in range(N)] for x in range(N): if parents[x]!=None: graph[parents[x]].append(x) else: root=x if leftright: queue=[root] left,right=[None]*N,[None]*N left[root]=0 right[root]=N while queue: x=queue.pop() for y in graph[x]: if ya and queue[-1][1]