This documentation is automatically generated by competitive-verifier/competitive-verifier
r"""
______________________
< it's hidehico's code >
----------------------
\
\
.--.
|o_o |
|:_/ |
// \ \
(| | )
/'\_ _/`\
\___)=(___/
"""
# ライブラリと関数と便利変数
# ライブラリ
import bisect
import copy
import heapq
import math
import sys
from collections import Counter, defaultdict, deque
from itertools import accumulate, combinations, permutations
from math import gcd, lcm, pi
from operator import itemgetter
from typing import Any, List, Tuple
# from atcoder.segtree import SegTree
# from atcoder.lazysegtree import LazySegTree
# from atcoder.dsu import DSU
# cortedcontainersは使うときだけ wandbox非対応なので
# from sortedcontainers import SortedDict, SortedSet, SortedList
# import pypyjit
# pypyjit.set_param("max_unroll_recursion=-1")
sys.setrecursionlimit(5 * 10**5)