import sys sys.setrecursionlimit(10**7) def ii(): return int(input()) def ist(): return input().split() def mi(d=0): return map(lambda x:int(x)-d,input().split()) def lmi(d=0): return list(map(lambda x:int(x)-d,input().split())) INF = 998244353 def answer(s): print(s) exit() def cross(xy): x,y = xy return (x+1,y),(x-1,y),(x,y+1),(x,y-1) ################################################ class SegTree: def __init__(self,n,inf,order,arr): self.inf = inf self.order = order self.bitlen = 2**n.bit_length() self.len = n self.n = self.bitlen*2-1 arr += [inf]*(self.bitlen - n) self.arr = [None]*(self.bitlen-1) + arr def PreProcessing(index): if self.arr[index] == None: self.arr[index] = self.order(PreProcessing(2*index+1),PreProcessing(2*index+2)) return self.arr[index] PreProcessing(0) #データ更新:index番目をxに変更 def Renew(self,index,x): i = self.n - self.bitlen + index self.arr[i] = x while i != 0: i = (i-1)//2 result = self.order(self.arr[i*2+1],self.arr[i*2+2]) if result != self.arr[i]: self.arr[i] = result def Swap(self,l,r): left,right = self.arr[self.n-self.bitlen+l],self.arr[self.n-self.bitlen+r] self.Renew(l,right) self.Renew(r,left) #[x,y)の範囲の結果を取得 def GetRange(self,x,y,k=0,l=0,r=-1): if r == -1: r = self.bitlen if y<=l or r<=x: return self.inf elif x<=l and r<=y: return self.arr[k] else: return self.order( self.GetRange(x,y,2*k+1,l,(l+r)//2), self.GetRange(x,y,2*k+2,(l+r)//2,r) ) def nibtan(self,x,min_left=0,max_right=-1): if max_right == -1: max_right = self.len k = 0 l,r = 0,self.bitlen while k < self.bitlen-1: left,right = self.arr[k*2+1],self.arr[k*2+2] c = (l+r)//2 if c <= min_left: l = c k = 2*k+2 elif c >= max_right: r = c k = 2*k+1 else: if left