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 class Segment_Tree: def __init__(self,N,f,e,lst=None,dynamic=False): self.f=f self.e=e self.N=N if dynamic: self.segment_tree=defaultdict(lambda:self.e) else: if lst==None: self.segment_tree=[self.e]*2*self.N else: assert len(lst)<=self.N self.segment_tree=[self.e]*self.N+[x for x in lst]+[self.e]*(N-len(lst)) for i in range(self.N-1,0,-1): self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1]) def __getitem__(self,i): if type(i)==int: if -self.N<=i<0: return self.segment_tree[i+self.N*2] elif 0<=i1: i>>= 1 self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1]) def Build(self,lst): for i,x in enumerate(lst,self.N): self.segment_tree[i]=x for i in range(self.N-1,0,-1): self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1]) def Fold(self,L=None,R=None): if L==None: L=self.N else: L+=self.N if R==None: R=self.N*2 else: R+=self.N vL=self.e vR=self.e while L>=1 R>>=1 return self.f(vL,vR) def Fold_Index(self,L=None,R=None): if L==None: L=self.N else: L+=self.N if R==None: R=self.N*2 else: R+=self.N if L==R: return None x=self.Fold(L-self.N,R-self.N) while L>=1 R>>=1 while i>=1 r>>=1 if f(self.f(vl,vr)): return self.N v=self.e while True: while L%2==0: L>>=1 vv=self.f(v,self.segment_tree[L]) if f(vv): v=vv L+=1 else: while L>=1 r>>=1 if f(self.f(vl,vr)): return 0 v=self.e while True: R-=1 while R>1 and R%2: R>>=1 vv=self.f(self.segment_tree[R],v) if f(vv): v=vv else: while R>k&1 and N!=None: N=self.permutation_doubling[k][N] return N def Doubling(self,N,K): if K<0: return self.e retu=self.e for k in range(self.k): if K>>k&1: if self.permutation_doubling[k][N]==None: return None retu=self.f(retu,self.doubling[k][N]) N=self.permutation_doubling[k][N] return N,retu def Bisect(self,x,is_ok): if not is_ok(x): return -1,None K=0 for k in range(self.k-1,-1,-1): if is_ok(self.permutation_doubling[k][x]): K|=1<