import sys, random input = lambda : sys.stdin.readline().rstrip() write = lambda x: sys.stdout.write(x+"\n"); writef = lambda x: print("{:.12f}".format(x)) debug = lambda x: sys.stderr.write(x+"\n") YES="Yes"; NO="No"; pans = lambda v: print(YES if v else NO); INF=10**18 LI = lambda : list(map(int, input().split())); II=lambda : int(input()) def debug(_l_): for s in _l_.split(): print(f"{s}={eval(s)}", end=" ") print() def dlist(*l, fill=0): if len(l)==1: return [fill]*l[0] ll = l[1:] return [dlist(*ll, fill=fill) for _ in range(l[0])] def z_algorithm(s): """ 各iについてs[0..n)とs[i..n)のLCP(Longest Common Prefix)の長さを求める s: str or (list of int ) """ n = len(s) if n==0: return [] z = [None]*n z[0] = 0 j = 0 for i in range(1,n): k = 0 if j + z[j] <= i else min(j+z[j]-i, z[i-j]) z[i] = k while i+k