from operator import itemgetter from itertools import * from bisect import * from collections import * from heapq import * import sys sys.setrecursionlimit(10**6) int1 = lambda x: int(x)-1 p2D = lambda x: print(*x, sep="\n") def II(): return int(sys.stdin.buffer.readline()) def MI(): return map(int, sys.stdin.buffer.readline().split()) def MI1(): return map(int1, sys.stdin.buffer.readline().split()) def LI(): return list(map(int, sys.stdin.buffer.readline().split())) def LI1(): return list(map(int1, sys.stdin.buffer.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def SI(): return sys.stdin.buffer.readline()[:-1] def LLI1(rows_number): return [LI1() for _ in range(rows_number)] dij = [(1, 0), (0, 1), (-1, 0), (0, -1)] def factors(a): if a<=0:return [0] low=[] high=[] for d in range(1,a+1): if d*d>a:break if a%d:continue low.append(d) high.append(a//d) if low[-1]==high[-1]:high.pop() return low+high[::-1] def nearf(a,s): if a<=s:return a if s**2a:break if a%d==0:return a//d for d in range(s1,0,-1): if a%d==0:return d def solve(a,b): ans=[] while a