import sys # sys.setrecursionlimit(200005) # sys.set_int_max_str_digits(200005) int1 = lambda x: int(x)-1 pDB = lambda *x: print(*x, end="\n", file=sys.stderr) p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr) def II(): return int(sys.stdin.readline()) def LI(): return list(map(int, sys.stdin.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def LI1(): return list(map(int1, sys.stdin.readline().split())) def LLI1(rows_number): return [LI1() for _ in range(rows_number)] def SI(): return sys.stdin.readline().rstrip() dij = [(0, 1), (-1, 0), (0, -1), (1, 0)] # dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)] # inf = -1-(-1 << 31) inf = -1-(-1 << 62) # md = 10**9+7 md = 998244353 class BitSum: def __init__(self, n): self._n = n+1 self._table = [0]*self._n def add(self, i, x): if x == 0: return i += 1 while i < self._n: self._table[i] += x i += i & -i def sum(self, r): res = 0 while r > 0: res += self._table[r] r -= r & -r return res def sumlr(self, l, r): if l >= r: return 0 if l == 0: return self.sum(r) return self.sum(r)-self.sum(l) def cnt_sum(l,r,border): bl=(l-1)//w+1 br=r//w if bl>br: s=c=0 for i in range(l,r): if aa[i]